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

Answer:

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

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

Step-by-step explanation:

Given the rational expression

$\dfrac{7x+5}{x-1} -(\dfrac{8x-1}{x-1} +\dfrac{2x-4}{x-1} )$

Let us first simplify before making our deductions.

Opening the brackets

$\dfrac{7x+5}{x-1} -(\dfrac{8x-1}{x-1} +\dfrac{2x-4}{x-1} )=\dfrac{7x+5}{x-1} -\dfrac{8x-1}{x-1} -\dfrac{2x-4}{x-1}$

Taking LCM

$=\dfrac{7x+5-(8x-1)-(2x-4)}{x-1}$

Opening the brackets and simplifying

$=\dfrac{7x+5-8x+1-2x+4}{x-1}\\\text{Collecting like terms in the numerator}\\=\dfrac{7x-8x-2x+5+1+4}{x-1}\\=\dfrac{-3x+10}{x-1}$

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.