Question

What expression is equivalent to the equation below?

Answer 1

ANSWER

$\frac{(2a + 1)^{2}}{50a}$

EXPLANATION

The given expression is

$\frac{2a + 1}{10a - 5} \div \frac{10a}{ \: 4 {a}^{2} - 1}$

Multiply by the reciprocal of the second function

$\frac{2a + 1}{10a - 5} \times \frac{4 {a}^{2} - 1}{ 10a}$

Rewrite the second numerator as difference of two squares.

$\frac{2a + 1}{10a - 5} \times \frac{( {2a})^{2} - {1}^{2} }{ 10a}$

Factor

$\frac{2a + 1}{5(2a - 1)} \times \frac{ (2a - 1)(2a + 1) }{ 10a}$

$\frac{2a + 1}{5} \times \frac{ (2a + 1) }{ 10a}$

Cancel out the common factors.

$\frac{(2a + 1)(2a + 1)}{50a}$

Simplify

$\frac{(2a + 1)^{2}}{50a}$