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# Subtracting rational expressions

Sal subtracts and simplifies (a-2)/(a+2) - (a-3)/(a²+4a+4). Created by Sal Khan.

## Want to join the conversation?

• at why did Sal make it into a difference of square, couldn't he have just left it as
(a+2)(a-2)(a-3)/(a+2)(a+2), then crossed out the (a+2)'s and simplified? (just curious)
• No he couldn't, listen carefully around at up to to see why.
The final answer is:
a²-a-1/(a+2)²
Because if we factor a²-a-1 it will not turn to (a+2)(a-2)(a-3). In fact if solve this using the quadratic equation you will see that it will factor into complex numbers.
• how come he didn't change + a-3/(a+2)(a+2) to -a-3/(a+2)(a+2) like that's what her did in those previous videos but when I changed the sign my answer came out different ! help someone please explain 😩😥😭😭😭😭
• The minus in front of the fraction applies to the entire numerator: - (a - 3)
Distribute the minus: - (a - 3) = -a + 3
Hope this helps.
• The question asks for me to Simplify and expand the following expression:
(5z−2)/(2z+2)−(z/3z−5)
When I put in the answer in this exact format
(13z^2 −33z+10)/(6z^2 −4z−10)

It tells me "Your answer is not fully expanded and simplified.", when I go look up the answer for the question is display the same answer yet it keeps telling me it's incorrect. Is there something i'm doing incorrect in the input?
• I am having the same issue with the last 2 tests in that section. I wrote it out the same way you did, the numbers in the numerator and denominator in parentheses divided by one another. I clicked on report the problem on both tests, so that they know there is a problem. You may want to try that too. If we are writing it out incorrectly, someone please reply.
• Good eve my given in denominator is the same how to solution them
• I had a question that was (7z^2)/(12z^3-4z^2) plus another rational expression. I pulled out 4z^2 to make it (7z^2)/ 4z^2(3z-1). Why is it wrong to cancel the two z^2 before adding?
• Based on the information you give, it isn't wrong to cancel them out --- BUT --- without seeing the entire problem and the rest of your work on it, I can't be sure why someone would have said it was wrong to cancel them out. ( Is it possible that not canceling them out would have made finding a common denominator easier?)
• how would i solve: 2x+1/x2+8x+16x-3/x2-16
• Hi Jennifer
If you are asking how to solve 2x+1/(x^2+8x+16x-3/x^2-16), than an example of how you would solve it goes like this where 2x+1 = a, x^2+24x-3 = b, and x^2-16 = c:
=a / (b/c)
=a/1 * c/b
=ac/b
So now let's re-arrange a, b, and c, using your numbers:
= ac / b
=(2x+1)(x^2-16) / x^2+8x+16
= (2x+1)(x+4)(x-4) / (x+4)(x+4)
cross out the x+4 in the numerator and the denominator because anything over itself = 1
=(2x+1)(x-4) / (x+4)

Hope this helps!
• 3 2 2
------- + ------- - -------
x (x-2) x^2
how would I solve this?
• How do I slove:
3x 2
-------- - -------
x-5 xsquared -25
Not really sure what the least Common Denominator is (i think it is (x+5)(x-5) not sure what to do from there
(1 vote)
• Bobby,
You have
3x/(x-5) - 2/(x²-25)
And you are correct that (x²-25) is (x+5)(x-5)
So you have
3x/(x+5) - 2/((x+5)(x-5))
The first fraction nneds to also have the same denominator, so
you want to multiply the first fraction by (x-5)(x-5)
3x(x-5) / ((x+5)(x-5)) - 2 / ((x+5)(x-5))
Distribute the 3x in the first fraction numerator
(3x²-15x) / ((x+5)(x-5)) - 2 / ((x+5)(x-5)) And combine the numerators
(3x²-15x-2) / ((x+5)(x-5))

I hope that helps make it click for you.
• I have just now completed the Algebra II course. However, there are a couple of sections I need to review before I take the Unit Test because I started taking the older version of Algebra II and then switched to the newer version of Algebra II and there are more topics covered in the new version of Algebra II.
But bottom line I have two questions concerning my continued math journey.

1. After I complete my review of Algebra II should I go directly to Pre-Calculus or Calculus since I completed Algebra II?

2. I took Geometry many years ago and don’t remember very much, if any, about the course. Should I take Geometry on Khan Academy before I start taking Pre-Calculus or Calculus?