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

Question

asked Jul 24, 2019 7.7k views

1 Answer

Rudi Strydom · Answer 1 · 2019-07-30T16:17:07+0000

Answer:

$=\frac {x+2}{x^2+2}$ 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.