Pre-Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Factor $z$ out of $z y$ .

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

Step 1.3

Factor $z$ out of $z \cdot z + z (y)$ .

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

Step 2

Cancel the common factor of $z + y$ .

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Step 2.1

Factor $z + y$ out of ${(z + y)}^{2}$ .

$\frac{(z + y) (z + y)}{z - y} \cdot \frac{z}{z (z + y)}$

Step 2.2

Factor $z + y$ out of $z (z + y)$ .

$\frac{(z + y) (z + y)}{z - y} \cdot \frac{z}{(z + y) z}$

Step 2.3

Cancel the common factor.

$\frac{(z + y) (z + y)}{z - y} \cdot \frac{z}{(z + y) z}$

Step 2.4

Rewrite the expression.

$\frac{z + y}{z - y} \cdot \frac{z}{z}$

Step 3

Multiply $\frac{z + y}{z - y}$ by $\frac{z}{z}$ .

$\frac{(z + y) z}{(z - y) z}$

Step 4

Cancel the common factor of $z$ .

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Step 4.1

Cancel the common factor.

$\frac{(z + y) z}{(z - y) z}$

Step 4.2

Rewrite the expression.

$\frac{z + y}{z - y}$