Basic Math Examples

$\frac{6 y - 30}{- 5 y} \cdot \frac{35}{45 - 9 y}$

Step 1

Simplify terms.

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Step 1.1

Factor $6$ out of $6 y - 30$ .

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Step 1.1.1

Factor $6$ out of $6 y$ .

$\frac{6 (y) - 30}{- 5 y} \cdot \frac{35}{45 - 9 y}$

Step 1.1.2

Factor $6$ out of $- 30$ .

$\frac{6 y + 6 \cdot - 5}{- 5 y} \cdot \frac{35}{45 - 9 y}$

Step 1.1.3

Factor $6$ out of $6 y + 6 \cdot - 5$ .

$\frac{6 (y - 5)}{- 5 y} \cdot \frac{35}{45 - 9 y}$

Step 1.2

Factor $9$ out of $45 - 9 y$ .

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Step 1.2.1

Factor $9$ out of $45$ .

$\frac{6 (y - 5)}{- 5 y} \cdot \frac{35}{9 (5) - 9 y}$

Step 1.2.2

Factor $9$ out of $- 9 y$ .

$\frac{6 (y - 5)}{- 5 y} \cdot \frac{35}{9 (5) + 9 (- y)}$

Step 1.2.3

Factor $9$ out of $9 (5) + 9 (- y)$ .

$\frac{6 (y - 5)}{- 5 y} \cdot \frac{35}{9 (5 - y)}$

Step 1.3

Cancel the common factor of $3$ .

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Step 1.3.1

Factor $3$ out of $6 (y - 5)$ .

$\frac{3 (2 (y - 5))}{- 5 y} \cdot \frac{35}{9 (5 - y)}$

Step 1.3.2

Factor $3$ out of $9 (5 - y)$ .

$\frac{3 (2 (y - 5))}{- 5 y} \cdot \frac{35}{3 (3 (5 - y))}$

Step 1.3.3

Cancel the common factor.

$\frac{3 (2 (y - 5))}{- 5 y} \cdot \frac{35}{3 (3 (5 - y))}$

Step 1.3.4

Rewrite the expression.

$\frac{2 (y - 5)}{- 5 y} \cdot \frac{35}{3 (5 - y)}$

Step 1.4

Cancel the common factor of $5$ .

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Step 1.4.1

Factor $5$ out of $- 5 y$ .

$\frac{2 (y - 5)}{5 (- y)} \cdot \frac{35}{3 (5 - y)}$

Step 1.4.2

Factor $5$ out of $35$ .

$\frac{2 (y - 5)}{5 (- y)} \cdot \frac{5 (7)}{3 (5 - y)}$

Step 1.4.3

Cancel the common factor.

$\frac{2 (y - 5)}{5 (- y)} \cdot \frac{5 \cdot 7}{3 (5 - y)}$

Step 1.4.4

Rewrite the expression.

$\frac{2 (y - 5)}{- y} \cdot \frac{7}{3 (5 - y)}$

Step 1.5

Multiply $\frac{2 (y - 5)}{- y}$ by $\frac{7}{3 (5 - y)}$ .

$\frac{2 (y - 5) \cdot 7}{- y (3 (5 - y))}$

Step 1.6

Multiply.

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Step 1.6.1

Multiply $7$ by $2$ .

$\frac{14 (y - 5)}{- y (3 (5 - y))}$

Step 1.6.2

Multiply $3$ by $- 1$ .

$\frac{14 (y - 5)}{- 3 y (5 - y)}$

Step 1.7

Cancel the common factor of $y - 5$ and $5 - y$ .

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Step 1.7.1

Factor $- 1$ out of $y$ .

$\frac{14 (- 1 (- y) - 5)}{- 3 y (5 - y)}$

Step 1.7.2

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{14 (- 1 (- y) - 1 (5))}{- 3 y (5 - y)}$

Step 1.7.3

Factor $- 1$ out of $- 1 (- y) - 1 (5)$ .

$\frac{14 (- 1 (- y + 5))}{- 3 y (5 - y)}$

Step 1.7.4

Reorder terms.

$\frac{14 (- 1 (- y + 5))}{- 3 y (- y + 5)}$

Step 1.7.5

Cancel the common factor.

$\frac{14 (- 1 (- y + 5))}{- 3 y (- y + 5)}$

Step 1.7.6

Rewrite the expression.

$\frac{14 \cdot (- 1)}{- 3 y}$

Step 2

Multiply $14$ by $- 1$ .

$\frac{- 14}{- 3 y}$

Step 3

Dividing two negative values results in a positive value.

$\frac{14}{3 y}$