Basic Math Examples

$\frac{6}{y} - 5 \cdot \frac{6}{6 - 5 y}$

Step 1

Multiply $- 5$ by $\frac{6}{6 - 5 y}$ .

$\frac{6}{y} - 5 \frac{6}{6 - 5 y}$

Step 2

Multiply $- 5 \frac{6}{6 - 5 y}$ .

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Step 2.1

Combine $- 5$ and $\frac{6}{6 - 5 y}$ .

$\frac{6}{y} + \frac{- 5 \cdot 6}{6 - 5 y}$

Step 2.2

Multiply $- 5$ by $6$ .

$\frac{6}{y} + \frac{- 30}{6 - 5 y}$

Step 3

Move the negative in front of the fraction.

$\frac{6}{y} - \frac{30}{6 - 5 y}$

Step 4

To write $\frac{6}{y}$ as a fraction with a common denominator, multiply by $\frac{6 - 5 y}{6 - 5 y}$ .

$\frac{6}{y} \cdot \frac{6 - 5 y}{6 - 5 y} - \frac{30}{6 - 5 y}$

Step 5

To write $- \frac{30}{6 - 5 y}$ as a fraction with a common denominator, multiply by $\frac{y}{y}$ .

$\frac{6}{y} \cdot \frac{6 - 5 y}{6 - 5 y} - \frac{30}{6 - 5 y} \cdot \frac{y}{y}$

Step 6

Write each expression with a common denominator of $y (6 - 5 y)$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{6}{y}$ by $\frac{6 - 5 y}{6 - 5 y}$ .

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

Step 6.2

Multiply $\frac{30}{6 - 5 y}$ by $\frac{y}{y}$ .

$\frac{6 (6 - 5 y)}{y (6 - 5 y)} - \frac{30 y}{(6 - 5 y) y}$

Step 6.3

Reorder the factors of $(6 - 5 y) y$ .

$\frac{6 (6 - 5 y)}{y (6 - 5 y)} - \frac{30 y}{y (6 - 5 y)}$

Step 7

Combine the numerators over the common denominator.

$\frac{6 (6 - 5 y) - 30 y}{y (6 - 5 y)}$

Step 8

Reorder terms.

$\frac{- 30 y + 6 (6 - 5 y)}{y (6 - 5 y)}$

Step 9

Rewrite $\frac{- 30 y + 6 (6 - 5 y)}{y (6 - 5 y)}$ in a factored form.

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Step 9.1

Factor $- 6$ out of $- 30 y + 6 (6 - 5 y)$ .

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Step 9.1.1

Reorder $6$ and $- 5 y$ .

$\frac{- 30 y + 6 (- 5 y + 6)}{y (6 - 5 y)}$

Step 9.1.2

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

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

Step 9.1.3

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

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

Step 9.1.4

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

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

Step 9.2

Apply the distributive property.

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

Step 9.3

Multiply $- 5$ by $- 1$ .

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

Step 9.4

Multiply $- 1$ by $6$ .

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

Step 9.5

Add $5 y$ and $5 y$ .

$\frac{- 6 (10 y - 6)}{y (6 - 5 y)}$

Step 9.6

Factor.

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Step 9.6.1

Factor $2$ out of $10 y - 6$ .

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Step 9.6.1.1

Factor $2$ out of $10 y$ .

$\frac{- 6 (2 (5 y) - 6)}{y (6 - 5 y)}$

Step 9.6.1.2

Factor $2$ out of $- 6$ .

$\frac{- 6 (2 (5 y) + 2 (- 3))}{y (6 - 5 y)}$

Step 9.6.1.3

Factor $2$ out of $2 (5 y) + 2 (- 3)$ .

$\frac{- 6 (2 (5 y - 3))}{y (6 - 5 y)}$

Step 9.6.2

Remove unnecessary parentheses.

$\frac{- 6 \cdot 2 (5 y - 3)}{y (6 - 5 y)}$

Step 9.7

Multiply $- 6$ by $2$ .

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