Question

which two of the following rational expressions equal - 1?
$\frac{4x + 5}{4x - 5}$ $\frac{4x - 5}{5 - 4x}$ $\frac{4x + 5}{5 + 4x}$ $\frac{4x + 5}{-4x - 5}$
select all that apply.
a. $\frac{4x + 5}{4x - 5}$
b. $\frac{4x + 5}{5 + 4x}$
c. $\frac{4x + 5}{-4x - 5}$
d. $\frac{4x - 5}{5 - 4x}$

Explanation:

Step1: Analyze option D

We can rewrite $\frac{4x - 5}{5 - 4x}$ as $\frac{-(5 - 4x)}{5 - 4x}$. Since $\frac{-(5 - 4x)}{5 - 4x}=- 1$ for $x
eq\frac{5}{4}$.

Step2: Analyze option C

We can rewrite $\frac{4x + 5}{-4x - 5}$ as $\frac{4x+5}{-(4x + 5)}$. Since $\frac{4x + 5}{-(4x + 5)}=-1$ for $x
eq-\frac{5}{4}$.

Answer:

C. $\frac{4x + 5}{-4x - 5}$, D. $\frac{4x - 5}{5 - 4x}$