I need help sovling this. It is a fraction.

Question

+5/x-1 + 2-x/x

I hope that you can understand what I wrote. Someone please help because I am new at this. Help!!!!

Answer 1

First find a common denominator

This common denominator will be

(x)(x-1)

then since the denominator of 5/(x-1) is missing x multiply x to 5 to get 5x.

since the denominator of (2-x)/x is missing (x-1) multiply (2-x) with (x-1) to get (2-x)(x-1)

Now add the numerators and put them over the denominator

5x+(2-x)(x-1) / x(x-1)

Now this needs to be cleaned up:

(2-x)(x-1) = -x^2 + 3x-2

-x^2 + 3x-2 +5x = -x^2+8x-2 for the numerator

There is no way to factor this neatly, so we will leave it as a quadratic and put it over the denominator which is already simplified.

SOLUTION:
-x^2+8x-2 / / x(x-1)