Question

What expression is equivalent to the equation below?

Answer 1

ANSWER


`((2a + 1)^(2))/(50a)`

Step-by-step explanation

The given expression is


`(2a + 1)/(10a - 5) / \frac{10a}{ \: 4 {a}^(2) - 1}`

Multiply by the reciprocal of the second function


`(2a + 1)/(10a - 5) * \frac{4 {a}^(2) - 1}{ 10a}`

Rewrite the second numerator as difference of two squares.


`(2a + 1)/(10a - 5) * \frac{( {2a})^(2) - {1}^(2) }{ 10a}`

Factor


`(2a + 1)/(5(2a - 1)) * ( (2a - 1)(2a + 1) )/( 10a)`


`(2a + 1)/(5) * ( (2a + 1) )/( 10a)`

Cancel out the common factors.


`((2a + 1)(2a + 1))/(50a)`

Simplify


`((2a + 1)^(2))/(50a)`