Answer:
[tex]\frac{(2+5x)(2-5x)}{2x(5x-6)}[/tex]
Step-by-step explanation:
Simplify the numerator:
Rewrite 4 as [tex]2^{2}[/tex]
[tex]\frac{2^{2}-25x^{2} }{10x^{2}-11x-x }[/tex]
Rewrite [tex]25^{2}[/tex] as [tex](5x)^{2}[/tex]
[tex]\frac{2^{2}-(5x)^{2} }{10x^{2} -11x-x}[/tex]
Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^{2} -b^{2} =(a+b)(a-b)[/tex] and b = 5x.
[tex]\frac{(2+5x)(2-(5x))}{10x^{2}-11x-x }[/tex]
Multiply 5 by -1.
[tex]\frac{(2+5x)(2-5x)}{10x^{2}-11x-x }[/tex]
Simplify the denominator:
Subtract x from -11x
[tex]\frac{(2+5x)(2-5x)}{10x^{2}-12x }[/tex]
Factor 2x out of [tex]10x^{2} -12x[/tex]
[tex]\frac{(2+5x)(2-5x)}{2x(5x-6)}[/tex]
