Question

17 multiple choice 1 point
which expression is equivalent to $\frac{16m^{2}-1}{4m-1}$; where $m \
eq \frac{1}{4}$
$\bigcirc$ $-4m$
$\bigcirc$ $4m + 1$
$\bigcirc$ $4m$
$\bigcirc$ $4m - 1$
$\bigcirc$ $4m - 2$
clear my selection
previous

Explanation:

Step1: Factor the numerator

Notice $16m^2 - 1$ is a difference of squares: $a^2 - b^2=(a-b)(a+b)$, so $16m^2 - 1=(4m-1)(4m+1)$

Step2: Cancel common factors

Since $m
eq\frac{1}{4}$, $4m-1
eq0$, so we can cancel $4m-1$ from numerator and denominator:
$\frac{(4m-1)(4m+1)}{4m-1}=4m+1$

Answer:

B. $4m + 1$