1. ## Factorizing & Simplifying

Hello peeps!

I know how to simplify simple equations...like 8/3(x-1) + 2/x-1 you just multiply x-1 with 3 and multiply 2 with 3...but how about simplifying harder question like...

4x/ 3x^2+7x-6 - x/3x^2-14x+8

I tried to factorize the first denomenator it's (3x-6)(x-1)..right?

I dunno how to factorize the second deno..and im not sure how to continue simplifying..i think ill know if i knew how to factorize the second deno..

Thanks.

2. Originally Posted by Pink_Apple
Hello peeps!

I know how to simplify simple equations...like 8/3(x-1) + 2/x-1 you just multiply x-1 with 3 and multiply 2 with 3...but how about simplifying harder question like...

4x/ 3x^2+7x-6 - x/3x^2-14x+8

I tried to factorize the first denomenator it's (3x-6)(x-1)..right?

I dunno how to factorize the second deno..and im not sure how to continue simplifying..i think ill know if i knew how to factorize the second deno..

Thanks.
The first think you need to do is learn to use brackets to make
the expressions unambiguous.

Do you mean - simplify:

4x/(3x^2+7x-6) - x/(3x^2-14x+8)

Then the first denominator does not factorise as you suggest as:

(3x-6)(x-1)=3x^2-7x+6.

In fact:

3x^2+7x-6=(x+3)(3x-2)

and:

3x^2-14x+8=(x-4)(3x-2).

This suggests you can start your simplification by taking out the common
factor 1/(3x-2).

RonL