Question

Which expression is equivalent to 2a+1/10a-5 / 10a/4a^2-1

Answer 1

Answer:

$\large\boxed{\dfrac{(2a+1)^2}{50a}}$

Step-by-step explanation:

$10a-5=5(2a-1)\\\\4a^2-1=2^2a^2-1^2=(2a)^2-1^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2a-1)(2a+1)\\\\\dfrac{2a+1}{10a-5}\div\dfrac{10a}{4a^2-1}=\dfrac{2a+1}{5(2a-1)}\div\dfrac{10a}{(2a-1)(2a+1)}\\\\=\dfrac{2a+1}{5(2a-1)}\cdot\dfrac{(2a-1)(2a+1)}{10a}\qquad\text{cancel}\ (2a-1)\\\\=\dfrac{2a+1}{5}\cdot\dfrac{2a+1}{10a}=\dfrac{(2a+1)^2}{50a}$

Answer 2

Answer:

The answer is D on edg

Hope this helps!