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Nataly_w [17]
4 years ago
13

What expression is equivalent to the equation below?

Mathematics
1 answer:
lord [1]4 years ago
5 0
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}
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