Question

For all $c\le \pm \frac{1}{5}$, simplify $\frac{5c^2-24c-5}{1-25c^2}$.

• A. $\frac{5c+1}{5+c}$
• B. $\frac{5+c}{5c+1}$
• C. $-\frac{5c-1}{5-c}$
• D. $-\frac{5-c}{5c-1}$
• E. $\frac{5-c}{5c-1}$

Answer 1

The correct option is E $\frac{5-c}{5c-1}$

Given $c\le \pm \frac{1}{5}$

The value of $\frac{5c^2-24c-5}{1-25c^2}$

$=\frac{5c^2-25c+c-5}{1-{\left(5c\right)}^2}$

$=\frac{(5c+1)(c-5)}{(1+5c)(1-5c)}$

$=\frac{5-c}{5c-1}$