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### Course: Integrated math 3>Unit 13

Lesson 7: Adding subtracting rational expressions intro

# Intro to adding rational expressions with unlike denominators

Sal rewrites a/b+c/d as a single rational expression.

## Want to join the conversation?

• is there a video anywhere where sal does fractional addition like 1/x+2/x+1? need help!
• Well, the problem you gave have the same concept the video above described. We need to have a common denominators first in order to add the two fractions. Since x is anything, the only multiple of (x+2) and (x+1) is (x+1)(x+2). You multiply the first fraction by (x+1) and will get (x+1)/(x+2)(x+1). The second fraction can be multiplied by x+2. You will get (x+2)/(x+1)(x+2).
Adding the fractions together, you will get x+1+x+2/(x+2)(x+1). Which is just 2x+3/x^2+3x+3. This is as simplified as possible. Hope that helped!
• in the question 1+x/y/x/y why does it not simplify to 1?
Why is y+x/x the answer ? does the x not cancel?
• Since dividing a number by a fraction is the same as multiplying the number by the reciprocal of the fraction 1+x/y/x/y = (1+x)/y * y/x. The y's cancel leaving (1+x)/x. Now, consider this example: (1+2)/2. According to the logic you suggest in your question, the 2's cancel out and the answer is 1, but that is incorrect. You need to do the 1+2 first, giving 3/2.

Remember, if you have multiple terms in the numerator that are being added and or subtracted, then you can not cancel them out with a single term in the denominator, the expression with additions/subtractions must be taken as a whole, therefore 1+x has nothing in common with x. If you had (1+x)/(1+x), then yes, the terms cancel and the result is 1.

You may want to review this:
http://www.purplemath.com/modules/rtnldefs2.htm
• I don't get what he means at ?
• he has to multiply that side by "b" so that the denominators are equal.
• Couldn't you just do this: bd(a/b + c/d) = ad + bc, where the bs and ds in the denominator cancel away? Really, is there any algebraic rule that this operation is violating?
• You are multiplying a basic property of math: the identify property of multiplication. It says we can multiply any number by 1 (or something that = 1) and we have an equivalent value.
"bd" does not = 1. You would have to multiply by "bd/bd" to be multiplying by a value = 1.

You may be trying to use a property of equations. Equations and inequalities have their own properties that allow us to multiply by any value as long as we multiple the entire equation by that value. But, `(ad+bc)/bd` is not an equation. So, we can't apply a property of equations.
• Came across this problem on another math site:

The difference between the numerator and the denominator of a fraction is 5. If 5 is added to the denominator, the fraction is decreased by 5/4
Find the fraction.

So the fraction equals something like n/n+5 and I set up an equation like this: n/n+10 = n/n+5 - 5/4.
The problem I have is I only know the difference between the numerator and the denominator is 5, so it could be n+5/n, n-5/n, n/n+5 or n/n-5, right? But when I get the answer to the question it claims that the only possible answer is n+5/n.

Anyone know why this might be?
• I don't quite understand what you mean, but i can walk you through the problem. This is what you do:

The problem says that "the difference between the numerator and denominator is 5," or, in other words:
n - d = 5
n = numerator, and d = denominator. If we rearrange it, we get:
n = 5 + d
So, our fraction, instead of being n/d, we have:
(5 + d)/d
since n and (5 + d) are equal. Now, the next part of the problem says that "if 5 is added to the denominator, the fraction is decrease by 5/4." So, we just add 5 to the bottom of the fraction, and set it equal to the original fraction minus 5/4. This gives us:
(5 + d)/(d + 5) = (5 + d)/d - 5/4
The two (5 + d)s cancel, and we are left with 1 on the right side of the equation. Now, we just get d by itself on one side:
1 = (5 + d)/d - 5/4
1 + 5/4 = (5 + d)/d
9/4 = (5 + d)/d
9/4d = 5 + d
9/4d - d = 5
5/4d = 5
d = 4
So, d equals 4. Now we just replace d with 4 in our equation we made above (n = 5 + d), and we get:
n = 5 + 4
n = 9
Finally, we put our two numbers in the fraction and we get:
n/d = 9/4
Hope this helps! :)
• It is not an equation, it is an expression because it is not equal to something, so it simplifies to
2/x+5/x^3 = (2x^3+5x)/x^4 = x(2x^2+5)/x^4 = (2x^2+5)/x^3
• I was just wandering if you can cancel down the bd in the denominator with the b and d in the numerator since divison and multiplication are commutative operations. So that you are left with a + c in the end?
• No, we can't cancel out the "bd" in denominator with the "b" and "d" in the numerator.
When we reduce fractions, we cancel out factors (things being multiplied).
In the answer: (db - da) / (abc), the db and the da in the numerator are not factors. They are terms (things being added/subtracted) since they are being subtracted with each other.

If you back up a step in the video, Sal had: d(b-a) / (abc)
This is the factored form. The numerator now has 2 factors: the "d" and the "(b-a)". There is no "d" in the denominator, so that can't be cancelled. And, there is no factor "(b-a)" in the denominator, so that also can't be cancelled. Thus, the fraction is fully reduced in it's current form.
Hope this helps.
• Sal is correct in saying you need to multiply the unlike denominators but for the numerators can he just say a+c?
(1 vote)
• No, that won't work. To create an equivalent fraction, you must multiply both the numerator & denominator by the same value.
For example: 1/2 = 1/2(5/5) = 5/10
If you take your approach, you would say that 1/2 = 1/10. They are not equal fractions.

Hope this helps.