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

Problem

(y2)/(y−3)⋅(y2−y−6)/(y2+y)

Solution

1. Factor the quadratic trinomial in the numerator of the second fraction by finding two numbers that multiply to −6 and add to −1

(y2−y−6)/(y2+y)=((y−3)*(y+2))/(y2+y)

2. Factor the denominator of the second fraction by taking out the greatest common factor, which is y

((y−3)*(y+2))/(y2+y)=((y−3)*(y+2))/(y*(y+1))

3. Multiply the two fractions together into a single expression.

(y2*(y−3)*(y+2))/((y−3)*y*(y+1))

4. Cancel the common factors (y−3) and y from the numerator and the denominator.

(y⋅y*(y−3)*(y+2))/((y−3)*y*(y+1))=(y*(y+2))/(y+1)

5. Distribute the y in the numerator to reach the final simplified form.

(y*(y+2))/(y+1)=(y2+2*y)/(y+1)

Final Answer

(y2)/(y−3)⋅(y2−y−6)/(y2+y)=(y2+2*y)/(y+1)

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