Question

Simplify this rational expression. 2x^2+5x+3/2x^2-x-3

Answer 1

`2x+3`/
`2x-3`

Explanation:

firstly we make two steps to simplify this question.

1st step: simplify
`2x^(2) +5x+3`

to simplify this we use factorization

`2x^(2) +2x+3x+3`

`2x(x+1) +3(x+1)`

`(2x+3) (x+1)` .....(1)

2nd step:simplify
`2x^(2) -x-3`

`2x^(2) +2x-3x-3`

`2x(x+1)-3(x+1)`

`(2x-3)(x+1)` .....(2)

now dividing (1) and (2), we get the answer

`2x+3/2x-3`