Simplify (x^2-2x-8)/(x^3+x^2-2x)

Problem

(x2−2*x−8)/(x3+x2−2*x)

Solution

1. Factor the numerator by finding two numbers that multiply to −8 and add to −2

x2−2*x−8=(x−4)*(x+2)

2. Factor the denominator by first pulling out the greatest common factor, which is x

x3+x2−2*x=x*(x2+x−2)

3. Factor the quadratic remaining in the denominator by finding two numbers that multiply to −2 and add to 1

x*(x2+x−2)=x*(x+2)*(x−1)

4. Rewrite the expression using the factored forms of the numerator and denominator.

((x−4)*(x+2))/(x*(x+2)*(x−1))

5. Cancel the common factor (x+2) from both the numerator and the denominator, noting that x≠−2

(x−4)/(x*(x−1))

6. Distribute the denominator to reach the final simplified form.

(x−4)/(x2−x)

Final Answer

(x2−2*x−8)/(x3+x2−2*x)=(x−4)/(x2−x)

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