Answer:
[tex] =\frac {x+2}{x^2+2} [/tex] is the simplest form of given expression.
Step-by-step explanation:
The given question is [tex]\frac{x^2+x-2}{x^3-x^2+2x-2} [/tex]
To solve the problem we have to group or split middle term and then factorise
[tex] \frac{x^2+(2x-x)-2}{(x^3-x^2)+(2x-2)} [/tex]
Taking [tex]x^2[/tex] common from first two terms of denominator and 2 from next two terms
[tex] = \frac{x^2+2x-x-2}{x^2(x-1)+2(x-1)} [/tex]
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
[tex] = \frac{ x(x+2)-1(x+2)}{(x-1)(x^2+2)} [/tex]
[tex] =\frac{(x+2)(x-1)}{(x-1)(x^2+2)} [/tex]
Now cancel out x-1 from both numerator and denominator we get
[tex] =\frac {x+2}{x^2+2} [/tex] is the required simplest form.
