Question

Simplify the rational expressions. State any excluded values.

1. 2x - 8/x - 4
A. 2; where x ≠ 4
B. x
C. -3/2
D.8; where x≠2

2. 4x - 8/ 4x + 20
A. x-2/4x + 20; where x ≠ - 5
B. x + 5 / x - 2 ; where x ≠ 2
C. x - 2/ x + 5; where x ≠ - 5
D. 4 (x+2/x-5); where x ≠ 5

Answer 1

State exclusions `before` you simplify.\[\Large\rm \frac{2x-8}{\color{red}{x-4}}\]The denominator is where we look for our excluded values.
We need to avoid letting our fraction take the form \(\Large\rm \dfrac{stuff}{0}\).
Dividing by zero is a no no!

So when we look for exclusions, we're looking for what value of x gives us this zero.\[\Large\rm \color{red}{x-4}=0\]Solve for x to find your excluded x value.

To simplify, factor a 2 out of each term in the numerator,\[\Large\rm \frac{2(x-4)}{x-4}\]Understand how to simplify from there?