Basic Math Examples

$\frac{\frac{1}{7} + \frac{4}{y}}{\frac{1}{9} - \frac{8}{y}}$

Step 1

Multiply the numerator and denominator of the fraction by $63 y$ .

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Step 1.1

Multiply $\frac{\frac{1}{7} + \frac{4}{y}}{\frac{1}{9} - \frac{8}{y}}$ by $\frac{63 y}{63 y}$ .

$\frac{63 y}{63 y} \cdot \frac{\frac{1}{7} + \frac{4}{y}}{\frac{1}{9} - \frac{8}{y}}$

Step 1.2

Combine.

$\frac{63 y (\frac{1}{7} + \frac{4}{y})}{63 y (\frac{1}{9} - \frac{8}{y})}$

Step 2

Apply the distributive property.

$\frac{63 y \frac{1}{7} + 63 y \frac{4}{y}}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $7$ .

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Step 3.1.1

Factor $7$ out of $63 y$ .

$\frac{7 (9 y) \frac{1}{7} + 63 y \frac{4}{y}}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.1.2

Cancel the common factor.

$\frac{7 (9 y) \frac{1}{7} + 63 y \frac{4}{y}}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.1.3

Rewrite the expression.

$\frac{9 y + 63 y \frac{4}{y}}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.2

Cancel the common factor of $y$ .

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Step 3.2.1

Factor $y$ out of $63 y$ .

$\frac{9 y + y \cdot 63 \frac{4}{y}}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.2.2

Cancel the common factor.

$\frac{9 y + y \cdot 63 \frac{4}{y}}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.2.3

Rewrite the expression.

$\frac{9 y + 63 \cdot 4}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.3

Multiply $63$ by $4$ .

$\frac{9 y + 252}{63 y \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.4

Cancel the common factor of $9$ .

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Step 3.4.1

Factor $9$ out of $63 y$ .

$\frac{9 y + 252}{9 (7 y) \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.4.2

Cancel the common factor.

$\frac{9 y + 252}{9 (7 y) \frac{1}{9} + 63 y (- \frac{8}{y})}$

Step 3.4.3

Rewrite the expression.

$\frac{9 y + 252}{7 y + 63 y (- \frac{8}{y})}$

Step 3.5

Cancel the common factor of $y$ .

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Step 3.5.1

Move the leading negative in $- \frac{8}{y}$ into the numerator.

$\frac{9 y + 252}{7 y + 63 y \frac{- 8}{y}}$

Step 3.5.2

Factor $y$ out of $63 y$ .

$\frac{9 y + 252}{7 y + y \cdot 63 \frac{- 8}{y}}$

Step 3.5.3

Cancel the common factor.

$\frac{9 y + 252}{7 y + y \cdot 63 \frac{- 8}{y}}$

Step 3.5.4

Rewrite the expression.

$\frac{9 y + 252}{7 y + 63 \cdot - 8}$

Step 3.6

Multiply $63$ by $- 8$ .

$\frac{9 y + 252}{7 y - 504}$

Step 4

Simplify with factoring out.

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Step 4.1

Factor $9$ out of $9 y + 252$ .

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Step 4.1.1

Factor $9$ out of $9 y$ .

$\frac{9 (y) + 252}{7 y - 504}$

Step 4.1.2

Factor $9$ out of $252$ .

$\frac{9 y + 9 \cdot 28}{7 y - 504}$

Step 4.1.3

Factor $9$ out of $9 y + 9 \cdot 28$ .

$\frac{9 (y + 28)}{7 y - 504}$

Step 4.2

Factor $7$ out of $7 y - 504$ .

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Step 4.2.1

Factor $7$ out of $7 y$ .

$\frac{9 (y + 28)}{7 (y) - 504}$

Step 4.2.2

Factor $7$ out of $- 504$ .

$\frac{9 (y + 28)}{7 y + 7 \cdot - 72}$

Step 4.2.3

Factor $7$ out of $7 y + 7 \cdot - 72$ .

$\frac{9 (y + 28)}{7 (y - 72)}$