Question

Simplify the complex rational expression

Answer 1

2( x +2 )

x+1

Explanation:

to add or subtract expressions expand them to make their denominators the same, multiply 1 time
`(x-2)/(x-2)`

since
`(x)/(x-2)` and
`(x-2)/(x-2)` have the same denominators add them by adding their numerators

combine x + x -2

factor
`x^(2)` - 4

to add or subtract expressions expand them and multiply by 1

have same denominator add them by adding their numerators

do the multiplications in 3 + ( x-2 )(x+2)

combine like terms in 3 +
`x^(2)` + 2x - 2x -4

divide
`(2x-2)/(x-2)` by
`(-1 + x^(2) )/((x-2)(x+2) )` multiplying
`(2x-2)/(x-2)`

cancel out x-2 in both numerator and denominator

factor the expression that are not already factored

cancel out x-1 in both numerator and denominator

expand the expression

Answer 2

`2(x+2)/x+1`

Explanation: