Question

Simplify expression X^2+x-2/x^3-x^2+2x-2

Answer 1

`=\frac {x+2}{x^2+2}` is the simplest form of given expression.

Explanation:

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

To solve the problem we have to group or split middle term and then factorise

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

Taking
`x^2` common from first two terms of denominator and 2 from next two terms

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

Now,taking x common from first two terms of numerator and -1 from next two terms and in denominator taking(x-1) common from both terms

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

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

Now cancel out x-1 from both numerator and denominator we get

`=\frac {x+2}{x^2+2}` is the required simplest form.