so multiply by (3x-4)(x-1)/(3x-4)(x-1)

the first fraction becomes:

(3x^2-4x)/(3x-4)(x-1)

the second fraction becomes:

(x^2-1)/(3x-4)(x-1)

add them to get:

(4x^2-4x-1)/(3x-4)(x-1)

And if you had trouble, you could have started off by trying to make both fractions resemble the answer in the back of the book i.e. the denominators.

In order to do this, multiply (x/x-1) by (3x-4/3x-4).

Also multiply (x+1/3x-4) by (x-1/x-1).

Notice that (3x-4/3x-4) and (x-1/x-1) both equal 1 (they are divided by themselves). So when you multiply the fractions by these new fractions, you are multiplying by 1.

I’ll start the first part for you.

(x/x-1)*(3x-4/3x-4) = (3x^2 – 4x / (x-1)(3x-4))