Question

Simplify the expression given below.x+2/4x²+5x+1*4x+1/x²-4

Answer 1

`(1)/(x^2 - x - 2)`

Explanation:

The given expression is

`(x+2)/(4x^2+5x+1)* (4x+1)/(x^2-4)`

Factorize the denominators.

`(x+2)/(4x^2+4x+x+1)* (4x+1)/(x^2-2^2)`

`(x+2)/(4x(x+1)+1(x+1))* (4x+1)/((x-2)(x+2))`
`[\because a^2-b^2=(a-b)(a+b)]`

`(x+2)/((x+1)(4x+1))* (4x+1)/((x-2)(x+2))`

Cancel out common factors.

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

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

On further simplification we get

`(1)/(x^2 - x - 2)`

Therefore, the simplified form of the given expression is
`(1)/(x^2 - x - 2)`.

Answer 2

Answer:
`\bold{(1)/((x+1)(x-2))}`

Explanation:

`(x+2)/(4x^2+5x+1)* (4x+1)/(x^2-4)\\\\\\\text{Factor the quadratics:}\\(x+2)/((4x+1)(x+1))* (4x+1)/((x-2)(x+2))\\\\\\\text{Simplify - cross out (4x+1) and (x+2):}\\(1)/((x+1)(x-2))`