Question

Simplify the following fraction: itle="\frac{4-25x^2}{10x^2-11x-6}" alt="\frac{4-25x^2}{10x^2-11x-6}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$\frac{(2+5x)(2-5x)}{2x(5x-6)}$

Step-by-step explanation:

Simplify the numerator:

Rewrite 4 as $2^{2}$

$\frac{2^{2}-25x^{2} }{10x^{2}-11x-x }$

Rewrite $25^{2}$ as $(5x)^{2}$

$\frac{2^{2}-(5x)^{2} }{10x^{2} -11x-x}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} -b^{2} =(a+b)(a-b)$ and b = 5x.

$\frac{(2+5x)(2-(5x))}{10x^{2}-11x-x }$

Multiply 5 by -1.

$\frac{(2+5x)(2-5x)}{10x^{2}-11x-x }$

Simplify the denominator:

Subtract x from -11x

$\frac{(2+5x)(2-5x)}{10x^{2}-12x }$

Factor 2x out of $10x^{2} -12x$

$\frac{(2+5x)(2-5x)}{2x(5x-6)}$