Simplify to the lowest terms (2x^2-22x)/(x^2-10x-11)

You should write the factored form of denominator, hence,
you need to find the zeroes of denominator such
that:

`x^2-10x-11 = 0`

You
need to use quadratic formula such that:

`x_(1,2) =
(10+-sqrt(100 + 4*11))/2`

`x_(1,2) =
(10+-sqrt144)/2`

`x_(1,2) =
(10+-12)/2`

`x_1 = 11 ; x_2 =
-1`

You may write the factored form of denominator such
that:

`x^2-10x-11 =
(x-11)(x+1)`

You need to factor out `2x`  to numerator such
that:

`2x^2-22x =
2x(x-11)`

You need to substitute `2x(x-11)`  for
`2x^2-22x`  and `(x-11)(x+1)`  for x^2-10x-11 such
that:

`(2x^2-22x)/(x^2-10x-11) =
(2x(x-11))/((x-11)(x+1))`

Reducing by factor `x-11` 
yields:

`(2x^2-22x)/(x^2-10x-11) =
2x/(x+1)`

Hence, simplifying the fraction to
its lowest terms yields `(2x^2-22x)/(x^2-10x-11) = 2x/(x+1).`