Pre-Algebra Examples

$\frac{- 36 y^{7} z^{3} + 12 y^{3} z^{5} - 8 y^{7} z^{6}}{4 y^{3} z^{5}}$

Step 1

Factor $4 y^{3} z^{3}$ out of $- 36 y^{7} z^{3} + 12 y^{3} z^{5} - 8 y^{7} z^{6}$ .

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Step 1.1

Factor $4 y^{3} z^{3}$ out of $- 36 y^{7} z^{3}$ .

$\frac{4 y^{3} z^{3} (- 9 y^{4}) + 12 y^{3} z^{5} - 8 y^{7} z^{6}}{4 y^{3} z^{5}}$

Step 1.2

Factor $4 y^{3} z^{3}$ out of $12 y^{3} z^{5}$ .

$\frac{4 y^{3} z^{3} (- 9 y^{4}) + 4 y^{3} z^{3} (3 z^{2}) - 8 y^{7} z^{6}}{4 y^{3} z^{5}}$

Step 1.3

Factor $4 y^{3} z^{3}$ out of $- 8 y^{7} z^{6}$ .

$\frac{4 y^{3} z^{3} (- 9 y^{4}) + 4 y^{3} z^{3} (3 z^{2}) + 4 y^{3} z^{3} (- 2 y^{4} z^{3})}{4 y^{3} z^{5}}$

Step 1.4

Factor $4 y^{3} z^{3}$ out of $4 y^{3} z^{3} (- 9 y^{4}) + 4 y^{3} z^{3} (3 z^{2})$ .

$\frac{4 y^{3} z^{3} (- 9 y^{4} + 3 z^{2}) + 4 y^{3} z^{3} (- 2 y^{4} z^{3})}{4 y^{3} z^{5}}$

Step 1.5

Factor $4 y^{3} z^{3}$ out of $4 y^{3} z^{3} (- 9 y^{4} + 3 z^{2}) + 4 y^{3} z^{3} (- 2 y^{4} z^{3})$ .

$\frac{4 y^{3} z^{3} (- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3})}{4 y^{3} z^{5}}$

Step 2

Cancel the common factor of $4$ .

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Step 2.1

Cancel the common factor.

$\frac{4 y^{3} z^{3} (- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3})}{4 y^{3} z^{5}}$

Step 2.2

Rewrite the expression.

$\frac{y^{3} z^{3} (- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3})}{y^{3} z^{5}}$

Step 3

Cancel the common factor of $y^{3}$ .

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Step 3.1

Cancel the common factor.

$\frac{y^{3} z^{3} (- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3})}{y^{3} z^{5}}$

Step 3.2

Rewrite the expression.

$\frac{z^{3} (- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3})}{z^{5}}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $z^{3}$ out of $z^{5}$ .

$\frac{z^{3} (- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3})}{z^{3} z^{2}}$

Step 4.2

Cancel the common factor.

$\frac{z^{3} (- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3})}{z^{3} z^{2}}$

Step 4.3

Rewrite the expression.

$\frac{- 9 y^{4} + 3 z^{2} - 2 y^{4} z^{3}}{z^{2}}$

Step 5

Factor $- 1$ out of $- 9 y^{4}$ .

$\frac{- (9 y^{4}) + 3 z^{2} - 2 y^{4} z^{3}}{z^{2}}$

Step 6

Factor $- 1$ out of $3 z^{2}$ .

$\frac{- (9 y^{4}) - (- 3 z^{2}) - 2 y^{4} z^{3}}{z^{2}}$

Step 7

Factor $- 1$ out of $- (9 y^{4}) - (- 3 z^{2})$ .

$\frac{- (9 y^{4} - 3 z^{2}) - 2 y^{4} z^{3}}{z^{2}}$

Step 8

Factor $- 1$ out of $- 2 y^{4} z^{3}$ .

$\frac{- (9 y^{4} - 3 z^{2}) - (2 y^{4} z^{3})}{z^{2}}$

Step 9

Factor $- 1$ out of $- (9 y^{4} - 3 z^{2}) - (2 y^{4} z^{3})$ .

$\frac{- (9 y^{4} - 3 z^{2} + 2 y^{4} z^{3})}{z^{2}}$

Step 10

Simplify the expression.

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Step 10.1

Rewrite $- (9 y^{4} - 3 z^{2} + 2 y^{4} z^{3})$ as $- 1 (9 y^{4} - 3 z^{2} + 2 y^{4} z^{3})$ .

$\frac{- 1 (9 y^{4} - 3 z^{2} + 2 y^{4} z^{3})}{z^{2}}$

Step 10.2

Move the negative in front of the fraction.

$- \frac{9 y^{4} - 3 z^{2} + 2 y^{4} z^{3}}{z^{2}}$