Basic Math Examples

$\frac{- 15 y^{6} + 12 y^{5} - 12}{3 y^{4}}$

Step 1

Cancel the common factor of $- 15 y^{6} + 12 y^{5} - 12$ and $3$ .

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Step 1.1

Factor $3$ out of $- 15 y^{6}$ .

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

Step 1.2

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

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

Step 1.3

Factor $3$ out of $3 (- 5 y^{6}) + 3 (4 y^{5})$ .

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

Step 1.4

Factor $3$ out of $- 12$ .

$\frac{3 (- 5 y^{6} + 4 y^{5}) + 3 \cdot - 4}{3 y^{4}}$

Step 1.5

Factor $3$ out of $3 (- 5 y^{6} + 4 y^{5}) + 3 (- 4)$ .

$\frac{3 (- 5 y^{6} + 4 y^{5} - 4)}{3 y^{4}}$

Step 1.6

Cancel the common factors.

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Step 1.6.1

Factor $3$ out of $3 y^{4}$ .

$\frac{3 (- 5 y^{6} + 4 y^{5} - 4)}{3 (y^{4})}$

Step 1.6.2

Cancel the common factor.

$\frac{3 (- 5 y^{6} + 4 y^{5} - 4)}{3 y^{4}}$

Step 1.6.3

Rewrite the expression.

$\frac{- 5 y^{6} + 4 y^{5} - 4}{y^{4}}$

Step 2

Factor $- 1$ out of $- 5 y^{6}$ .

$\frac{- (5 y^{6}) + 4 y^{5} - 4}{y^{4}}$

Step 3

Factor $- 1$ out of $4 y^{5}$ .

$\frac{- (5 y^{6}) - (- 4 y^{5}) - 4}{y^{4}}$

Step 4

Factor $- 1$ out of $- (5 y^{6}) - (- 4 y^{5})$ .

$\frac{- (5 y^{6} - 4 y^{5}) - 4}{y^{4}}$

Step 5

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- (5 y^{6} - 4 y^{5}) - 1 (4)}{y^{4}}$

Step 6

Factor $- 1$ out of $- (5 y^{6} - 4 y^{5}) - 1 (4)$ .

$\frac{- (5 y^{6} - 4 y^{5} + 4)}{y^{4}}$

Step 7

Simplify the expression.

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Step 7.1

Rewrite $- (5 y^{6} - 4 y^{5} + 4)$ as $- 1 (5 y^{6} - 4 y^{5} + 4)$ .

$\frac{- 1 (5 y^{6} - 4 y^{5} + 4)}{y^{4}}$

Step 7.2

Move the negative in front of the fraction.

$- \frac{5 y^{6} - 4 y^{5} + 4}{y^{4}}$