Simplify (y^2)/(y-3)*(y^2-y-6)/(y^2+1y)

$\frac{y^{2}}{y - 3} \cdot \frac{y^{2} - y - 6}{y^{2} + 1 y}$

Step 1

Factor $y^{2} - y - 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y^{2} + 1 y}$

Step 2

Simplify terms.

Factor $y$ out of $y^{2} + 1 y$ .

Factor $y$ out of $y^{2}$ .

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y \cdot y + 1 y}$

Factor $y$ out of $1 y$ .

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y \cdot y + y \cdot 1}$

Factor $y$ out of $y \cdot y + y \cdot 1$ .

$\frac{y^{2}}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y (y + 1)}$

Cancel the common factor of $y$ .

Factor $y$ out of $y^{2}$ .

$\frac{y \cdot y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y (y + 1)}$

Cancel the common factor.

$\frac{y \cdot y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y (y + 1)}$

Rewrite the expression.

$\frac{y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y + 1}$

Cancel the common factor of $y - 3$ .

Cancel the common factor.

$\frac{y}{y - 3} \cdot \frac{(y - 3) (y + 2)}{y + 1}$

Rewrite the expression.

$y \cdot \frac{y + 2}{y + 1}$

Combine $y$ and $\frac{y + 2}{y + 1}$ .

$\frac{y (y + 2)}{y + 1}$

Simplify (y^2)/(y-3)*(y^2-y-6)/(y^2+1y)

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