https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:reducing-rational-expressions-to-lowest-terms/a/intro-to-rational-expressions 2023-07-18T22:48:45.033562364Z Intro to rational expressions Learn what rational expressions are and about the values for which they are undefined. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:reducing-rational-expressions-to-lowest-terms/v/simplifying-rational-expressions-introduction 2026-07-05T06:10:45.281152056Z Reducing rational expressions to lowest terms Learn how to simplify rational expressions, which are fractions with variable expressions in the numerator and denominator. This video also shows how to factor the expressions and cancel out common factors, just like with rational numbers. Don't forget to exclude values of x that would make the denominator zero, since those would make the expression undefined. Sal Khan video https://cdn.kastatic.org/googleusercontent/7_xnrQPhEysk9lgK10Vd9NIDtcPwUbz5gMfct17TDukM34SFLdyc20hgX0MJJoAO9Y5D6Kanqh5e9IYKqyfVPng Reducing rational expressions to lowest terms Learn how to simplify rational expressions, which are fractions with variable expressions in the numerator and denominator. This video also shows how to factor the expressions and cancel out common factors, just like with rational numbers. Don't forget to exclude values of x that would make the denominator zero, since those would make the expression undefined. https://cdn.kastatic.org/ka-youtube-converted/7Uos1ED3KHI.mp4/7Uos1ED3KHI.mp4 448 Rational algebraic expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:reducing-rational-expressions-to-lowest-terms/e/simplifying_rational_expressions_2 2024-02-19T03:57:27.509159735Z Reduce rational expressions to lowest terms Factor the numerator and the denominator of a rational expression and cancel out common binomial terms. Tomer Gal exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:reducing-rational-expressions-to-lowest-terms/a/reducing-rational-expressions-to-lowest-terms 2022-07-28T20:15:54.254459559Z Reducing rational expressions to lowest terms Learn what it means to reduce a rational expression to lowest terms, and how it's done! article https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:common-factors/v/simplifying-rational-expressions-w-common-monomial-factors 2022-10-07T01:44:59.407126867Z Simplifying rational expressions: common monomial factors Sal simplifies the rational expressions (14x²+7x)/(14x) and (17z³+17z²)/(34z³-51z²) by taking common factors and canceling them. video https://cdn.kastatic.org/ka_thumbnails_cache/5cd375fc-62cb-4880-9ad6-f951d5e93de6_1280_720_base.png Simplifying rational expressions: common monomial factors Sal simplifies the rational expressions (14x²+7x)/(14x) and (17z³+17z²)/(34z³-51z²) by taking common factors and canceling them. https://cdn.kastatic.org/ka-youtube-converted/XFwQV-KCudw.mp4/XFwQV-KCudw.mp4 419 Rational algebraic expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:reducing-rational-expressions-to-lowest-terms/e/simplifying_rational_expressions_1 2021-07-29T20:12:07.191455011Z Reduce rational expressions to lowest terms: Error analysis Analyze other people's attempts to reduce rational expressions to lowest terms, and identify the mistake they made. Tomer Gal exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/a/intro-to-adding-subtracting-rational-expressions 2021-06-30T17:32:36Z Intro to adding & subtracting rational expressions Learn how to add or subtract two rational expressions into a single expression. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/v/adding-and-subtracting-rational-expressions-with-like-denominators 2022-10-07T00:22:18.752150461Z Adding & subtracting rational expressions: like denominators Sal adds 6/(2x²-7) + (-3x-8)/(2x²-7) and subtracts (9x²+3)/(14x²-9) - (-3x²+5)/(14x²-9). video https://cdn.kastatic.org/ka_thumbnails_cache/85106a45-5c46-4a67-adc1-09325b01c8ce_1280_720_base.png Adding & subtracting rational expressions: like denominators Sal adds 6/(2x²-7) + (-3x-8)/(2x²-7) and subtracts (9x²+3)/(14x²-9) - (-3x²+5)/(14x²-9). https://cdn.kastatic.org/ka-youtube-converted/rmYlCuiC5uY.mp4/rmYlCuiC5uY.mp4 225 Rational algebraic expressions https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-add-sub-intro/e/adding_and_subtracting_rational_expressions 2021-07-03T00:17:26Z Add & subtract rational expressions: like denominators Example: Add and simplify 6/(2x²-7) + (-3x-8)/(2x²-7). Tomer Gal exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/v/algebraic-expression-adding-fractions 2021-06-30T17:32:39Z Intro to adding rational expressions with unlike denominators Sal rewrites a/b+c/d as a single rational expression. video https://cdn.kastatic.org/googleusercontent/PYfPwpfuJ06QaBU1vPvHpqVxVviV3-iFKdhrPnDdPyiAyV8ynryFvMbzHcf2ptLyWpEz6rFeEdoYFfIpLW0GkbWn Intro to adding rational expressions with unlike denominators Sal rewrites a/b+c/d as a single rational expression. https://cdn.kastatic.org/ka-youtube-converted/w7NhLkQynS8.mp4/w7NhLkQynS8.mp4 164 Rational algebraic expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/v/adding-rational-expression-w-unlike-denominators 2023-07-18T22:48:45.033562364Z Adding rational expression: unlike denominators Learn how to add rational expressions with different denominators by finding a common denominator, multiplying the numerators and denominators by the same factors, and simplifying the result. A rational expression is a fraction with polynomials in the numerator and denominator. video https://cdn.kastatic.org/ka_thumbnails_cache/2c85bd5c-ac01-4376-a390-d16d558cfbef_1280_720_base.png Adding rational expression: unlike denominators Learn how to add rational expressions with different denominators by finding a common denominator, multiplying the numerators and denominators by the same factors, and simplifying the result. A rational expression is a fraction with polynomials in the numerator and denominator. https://cdn.kastatic.org/ka-youtube-converted/DrE_iiw1Mvk.mp4/DrE_iiw1Mvk.mp4 311 Rational algebraic expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/v/subtracting-rational-expressions-w-unlike-denominators 2023-03-06T04:04:06.526793194Z Subtracting rational expressions: unlike denominators Sal rewrites (-5x)/(8x+7)-(6x³)/(3x+1) as (-48x⁴-42x³-15x²-5x)/(8x+7)(3x+1). video https://cdn.kastatic.org/ka_thumbnails_cache/06660b10-55fe-4be9-b0ab-04d2a12a8fc7_1280_720_base.png Subtracting rational expressions: unlike denominators Sal rewrites (-5x)/(8x+7)-(6x³)/(3x+1) as (-48x⁴-42x³-15x²-5x)/(8x+7)(3x+1). https://cdn.kastatic.org/ka-youtube-converted/evmDZkDvlNw.mp4/evmDZkDvlNw.mp4 287 Rational algebraic expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/v/subtracting-rational-expressions-w-factored-denominators 2022-10-07T00:22:18.752150461Z Subtracting rational expressions: factored denominators Sal subtracts two rational expressions whose denominators are factored. The denominators aren't the same but they share a factor. video https://cdn.kastatic.org/ka_thumbnails_cache/e31ef292-a8ba-4197-816a-eb3e397cef4b_1280_720_base.png Subtracting rational expressions: factored denominators Sal subtracts two rational expressions whose denominators are factored. The denominators aren't the same but they share a factor. https://cdn.kastatic.org/ka-youtube-converted/j8cKFzj5V6g.mp4/j8cKFzj5V6g.mp4 288 Rational algebraic expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:adding-and-subtracting-rational-expressions/e/adding_and_subtracting_rational_expressions_2 2022-07-28T20:15:54.254459559Z Add & subtract rational expressions (basic) Add and subtract rational expressions whose denominators don't have any shared factors. Tomer Gal exercise https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-mul-div/a/multiplying-rational-expressions 2021-06-29T20:27:49Z Multiplying rational expressions Learn how to find the product of two rational expressions. article https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-mul-div/a/dividing-rational-expressions 2021-06-29T20:27:49Z Dividing rational expressions Learn how to find the quotient of two rational expressions. article https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:multiplying-and-dividing-rational-expressions/v/multiplying-and-dividing-rational-expressions-monomial-numerator-denominator 2021-06-30T17:32:39Z Multiplying & dividing rational expressions: monomials Sal multiplies (6x³/5) X (2/3x) and divides (2x⁴/7) ➗ (5x⁴/4). video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Multiplying & dividing rational expressions: monomials Sal multiplies (6x³/5) X (2/3x) and divides (2x⁴/7) ➗ (5x⁴/4). https://cdn.kastatic.org/ka-youtube-converted/6nALFmvvgds.mp4/6nALFmvvgds.mp4 356 Rational algebraic expressions https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-mul-div/v/multiplying-and-dividing-rational-expressions-2 2021-06-29T20:27:58Z Multiplying rational expressions Sal multiplies and simplifies (a²-4)/(a²-1) X (a+1)/(a+2). Sal Khan video https://cdn.kastatic.org/googleusercontent/72YYlaXXFd1ihd2iakNpcNBgpERUNmDPqbR_zeMyILzhTGljRhdysT7yRYf6XJSYPjbc5ejmlRNUOupVZDRV8zk- Multiplying rational expressions Sal multiplies and simplifies (a²-4)/(a²-1) X (a+1)/(a+2). https://cdn.kastatic.org/ka-youtube-converted/f-wz_ZzSDdg.mp4/f-wz_ZzSDdg.mp4 292 Rational algebraic expressions https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-mul-div/v/multiplying-and-dividing-rational-expressions-3 2021-06-29T20:27:58Z Dividing rational expressions Sal divides and simplifies (2p+6)/(p+5) ➗ (10)/(4p+20). Sal Khan video https://cdn.kastatic.org/googleusercontent/Ek6-xhT6VAJKtxhdccTt040Jl3RqAcjE2i_RFpakMLH8U_4bHKthfu5NBmitodCVg8gEC6dIAeG4kXgyFyGuqLE Dividing rational expressions Sal divides and simplifies (2p+6)/(p+5) ➗ (10)/(4p+20). https://cdn.kastatic.org/ka-youtube-converted/gcnk8TnzsLc.mp4/gcnk8TnzsLc.mp4 250 Rational algebraic expressions https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-mul-div/v/multiplying-and-dividing-rational-expressions-1 2021-06-29T20:27:58Z Multiplying rational expressions: multiple variables Sal multiplies and simplifies (3x²y)/(2ab) X (14a²b)/(18xy²). Sal Khan video https://cdn.kastatic.org/googleusercontent/wWWhv79619rUfUjZCNTIvQNVnSXr783VzvpoKP-VFkfF-CLKYqapwdgawahpr4q2selDBR0Sir6kq3KS7eWxESg Multiplying rational expressions: multiple variables Sal multiplies and simplifies (3x²y)/(2ab) X (14a²b)/(18xy²). https://cdn.kastatic.org/ka-youtube-converted/3GL69IA2q4s.mp4/3GL69IA2q4s.mp4 218 Rational algebraic expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:multiplying-and-dividing-rational-expressions/e/multiplying_and_dividing_rational_expressions_1 2026-05-05T18:10:50.367167117Z Multiply & divide rational expressions: Error analysis Analyze other people's attempts to multiply and divide rational expressions, and identify the mistake they made. Tomer Gal exercise https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-mul-div/v/dividing-rational-expressions-w-unknown-expression 2022-10-07T01:44:59.407126867Z Dividing rational expressions: unknown expression Sal finds the polynomial D for which (20y²-80)/D ÷ (4y²-8y)/(y³+9y²)=1 is true for all values of y for which it's defined. video https://cdn.kastatic.org/ka_thumbnails_cache/45f576bd-e1a5-4352-86a4-41bf65477b59_1280_720_base.png Dividing rational expressions: unknown expression Sal finds the polynomial D for which (20y²-80)/D ÷ (4y²-8y)/(y³+9y²)=1 is true for all values of y for which it's defined. https://cdn.kastatic.org/ka-youtube-converted/54ZFp4CwWEg.mp4/54ZFp4CwWEg.mp4 362 Rational algebraic expressions https://www.khanacademy.org/math/math3/x5549cc1686316ba5:rationals/x5549cc1686316ba5:rational-mul-div/e/multiplying_and_dividing_rational_expressions_3 2025-02-27T11:46:16.621461116Z Multiply & divide rational expressions (advanced) Example: Multiply and simplify (3x²y)/(2ab) X (14a²b)/(18xy²). Tomer Gal exercise