Simplify the following fraction: (4-25x^2)/(10x^2-11x-6)

Question

Simplify the following fraction:
`(4-25x^2)/(10x^2-11x-6)`

Answer 1

`((2+5x)(2-5x))/(2x(5x-6))`

Explanation:

Simplify the numerator:

Rewrite 4 as
`2^(2)`

`(2^(2)-25x^(2)  )/(10x^(2)-11x-x )`

Rewrite
`25^(2)` as
`(5x)^(2)`

`(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.

`((2+5x)(2-(5x)))/(10x^(2)-11x-x )`

Multiply 5 by -1.

`((2+5x)(2-5x))/(10x^(2)-11x-x )`

Simplify the denominator:

Subtract x from -11x

`((2+5x)(2-5x))/(10x^(2)-12x )`

Factor 2x out of
`10x^(2) -12x`

`((2+5x)(2-5x))/(2x(5x-6))`