Question

Pls help!
Simplify:
5x
x² + 3x-4-x+1
[?]x² -
+ [ ]x - [
X

Answer 1

`\displaystyle (-1x^2-4)/(x^2+3x-4)`

Explanation:

To subtract these rational expressions we will find common denominators and then subtract. Then, we can factor to simplify. Lastly, we will multiply to meet the given answer format.

Given:

`\displaystyle (5x)/(x^2+3x-4) -(x+1)/(x-1)`

Common denominators:

`\displaystyle ((5x)(x-1))/((x^2+3x-4)(x-1)) -((x^2+3x-4)(x+1))/((x^2+3x-4)(x-1))`

Multiply each out:

`\displaystyle (5x^2-5x)/(x^3+2x^2-7x+4) -(x^3+4x^2-x-4)/(x^3+2x^2-7x+4)`

Subtract:

`\displaystyle (5x^2-5x-(x^3+4x^2-x-4))/(x^3+2x^2-7x+4)`

`\displaystyle (5x^2-5x-x^3-4x^2+x+4)/(x^3+2x^2-7x+4)`

`\displaystyle (-x^3+x^2-4x+4)/(x^3+2x^2-7x+4)`

Factor:

`\displaystyle (-(x-1)(x^2+4))/((x-1)^2(x+4))`

Cancel out terms in the numerator and denominator:

`\displaystyle (-(x^2+4))/((x-1)(x+4))`

Multiply factors back out to meet the answer format:

`\displaystyle (-1x^2-4)/(x^2+3x-4)`