Question

Add and subtract the rational expressions. 7x+5/x-1 -(8x1/x-1+2x-4/x-1) Which statements are true about the process for adding and subtracting the rational expressions? Select three options. 1. The expression is not defined when x = –1. The first step in the simplification is . 2. The denominator of the fully simplified expression will be x – 1. 3. The numerator of the fully simplified expression will be –3x. 4. The numerator of the fully simplified expression will be –3x + 10.

Answer 1

B , D

Explanation:

Correct on edge 2021. Just took the test, have a good day <3

Answer 2

2. The denominator of the fully simplified expression will be x – 1.

4. The numerator of the fully simplified expression will be –3x + 10.

Explanation:

Given the rational expression

`(7x+5)/(x-1) -((8x-1)/(x-1) +(2x-4)/(x-1) )`

Let us first simplify before making our deductions.

Opening the brackets

`(7x+5)/(x-1) -((8x-1)/(x-1) +(2x-4)/(x-1) )=(7x+5)/(x-1) -(8x-1)/(x-1) -(2x-4)/(x-1)`

Taking LCM

`=(7x+5-(8x-1)-(2x-4))/(x-1)`

Opening the brackets and simplifying

`=(7x+5-8x+1-2x+4)/(x-1)\\\text{Collecting like terms in the numerator}\\=(7x-8x-2x+5+1+4)/(x-1)\\=(-3x+10)/(x-1)`

The following statements are therefore true:

2. The denominator of the fully simplified expression will be x – 1.

4. The numerator of the fully simplified expression will be –3x + 10.