Answer:
[tex]\frac{x^2+x-2}{x^3-x^2+2x-2}\\=\frac{x^2+(2-1)x-2}{x^2(x-1)+2(x-1)}\\=\frac{x^2+2x-x-2}{(x-1)(x^2+2)}\\=\frac{x(x+2)-1(x+2)}{(x-1)(x^2+2)}\\=\frac{(x-1)(x+2)}{(x-1)(x^2+2)} \\=\frac{x+2}{x^2+2}\\So, ~last~option~is~the~correct~answer.[/tex]
The simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.
It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm \dfrac{\left(x^2+x-2\right)}{x^3-x^2+2x-2}[/tex]
[tex]\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{x^3-x^2+2x-2}[/tex]
[tex]\rm =\dfrac{\left(x-1\right)\left(x+2\right)}{\left(x-1\right)\left(x^2+2\right)}[/tex]
= (x + 2)/(x² + 2)
Thus, the simplest form of the provided expression is (x + 2)/(x² + 2) option (D) is correct.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ5
