What is (x^2+x-2)/(x^3-x^2-x+1) ?

The solution to (x^2+x-2)/(x^3-x^2-x+1) is (x+2)/((x-1)(x+1))

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simplify (x^2+x-2)/(x^3-x^2-x+1)

simplify

\frac{x ^{2} + x - 2}{x ^{3} - x ^{2} - x + 1}

\frac{x + 2}{( x - 1 ) ( x + 1 )}

Solution steps

\frac{x ^{2} + x - 2}{x ^{3} - x ^{2} - x + 1}

Factor

x^{2} + x - 2 : (x - 1) (x + 2)

= \frac{( x - 1 ) ( x + 2 )}{x ^{3} - x ^{2} - x + 1}

Factor

x^{3} - x^{2} - x + 1 : (x - 1)^{2} (x + 1)

= \frac{( x - 1 ) ( x + 2 )}{( x - 1 ) ^{2} ( x + 1 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(x - 1)^{2} = (x - 1) (x - 1)

= \frac{( x - 1 ) ( x + 2 )}{( x - 1 ) ( x - 1 ) ( x + 1 )}

Cancel the common factor:

x - 1

= \frac{x + 2}{( x - 1 ) ( x + 1 )}

49 \div 7

(- 10 - 4 i) - (6 + 9 i)

i^{124}

(n + 6)^{2}

\frac{25}{45}

What is (x^2+x-2)/(x^3-x^2-x+1) ?
The solution to (x^2+x-2)/(x^3-x^2-x+1) is (x+2)/((x-1)(x+1))