Simplify (x^2-x-6)/(x^2+2x)*(x^3+x^2)/(x^2-2x-3)

Problem

(x^2−x−6)/(x^2+2*x)⋅(x^3+x^2)/(x^2−2*x−3)

Solution

1. Factor the first numerator x^2−x−6 by finding two numbers that multiply to −6 and add to −1

(x−3)*(x+2)

2. Factor the first denominator x^2+2*x by taking out the greatest common factor x

x*(x+2)

3. Factor the second numerator x^3+x^2 by taking out the greatest common factor x^2

x^2*(x+1)

4. Factor the second denominator x^2−2*x−3 by finding two numbers that multiply to −3 and add to −2

(x−3)*(x+1)

5. Rewrite the entire expression using the factored forms.

((x−3)*(x+2))/(x*(x+2))⋅(x^2*(x+1))/((x−3)*(x+1))

6. Cancel the common factors (x−3) (x+2) and (x+1) from the numerators and denominators.

1/x⋅(x^2)/1

7. Simplify the remaining expression by dividing x^2 by x

x

Final Answer

(x^2−x−6)/(x^2+2*x)⋅(x^3+x^2)/(x^2−2*x−3)=x

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