Question

Simplify the expression given below x^2+x-2/x^3-x^2+2x-2

Answer 1

The solution is
`(x+2)/(x^2+2)`

Step-by-step explanation:

See the image attached

Answer 2

The simplest form is
`(x+2)/(x^2+2)`

Step-by-step explanation:

The given is:
`(x^2 + x-2)/(x^3-x^2+2x+2)`

1- For the numerator:

`x^2+x-2` can be factorized to give (x-1)(x+2)

2- For the denominator:

`x^3-x^2+2x-2`

We will factor this using grouping

Take
`x^2` as a common factor from the first two terms and
`2` as a common factor from the last two terms

This will give us:

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

Now, take (x-1) as a common factor:

`x^3-x^2+2x-2` = (x-1)(x²+2)

3- Finally, getting the simplest form:

`(x^2+x-2)/(x^3-x^2+2x-2)=((x-1)(x+2))/((x-1)(x^2+2))=(x+2)/(x^2+2)`

Hope this helps :)