Basic Math Examples

$\frac{9}{14 y^{2}} - \frac{9}{5 y}$

Step 1

To write $\frac{9}{14 y^{2}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{9}{14 y^{2}} \cdot \frac{5}{5} - \frac{9}{5 y}$

Step 2

To write $- \frac{9}{5 y}$ as a fraction with a common denominator, multiply by $\frac{14 y}{14 y}$ .

$\frac{9}{14 y^{2}} \cdot \frac{5}{5} - \frac{9}{5 y} \cdot \frac{14 y}{14 y}$

Step 3

Write each expression with a common denominator of $70 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{9}{14 y^{2}}$ by $\frac{5}{5}$ .

$\frac{9 \cdot 5}{14 y^{2} \cdot 5} - \frac{9}{5 y} \cdot \frac{14 y}{14 y}$

Step 3.2

Multiply $5$ by $14$ .

$\frac{9 \cdot 5}{70 y^{2}} - \frac{9}{5 y} \cdot \frac{14 y}{14 y}$

Step 3.3

Multiply $\frac{9}{5 y}$ by $\frac{14 y}{14 y}$ .

$\frac{9 \cdot 5}{70 y^{2}} - \frac{9 (14 y)}{5 y (14 y)}$

Step 3.4

Multiply $14$ by $5$ .

$\frac{9 \cdot 5}{70 y^{2}} - \frac{9 (14 y)}{70 y \cdot y}$

Step 3.5

Raise $y$ to the power of $1$ .

$\frac{9 \cdot 5}{70 y^{2}} - \frac{9 (14 y)}{70 (y^{1} y)}$

Step 3.6

Raise $y$ to the power of $1$ .

$\frac{9 \cdot 5}{70 y^{2}} - \frac{9 (14 y)}{70 (y^{1} y^{1})}$

Step 3.7

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{9 \cdot 5}{70 y^{2}} - \frac{9 (14 y)}{70 y^{1 + 1}}$

Step 3.8

Add $1$ and $1$ .

$\frac{9 \cdot 5}{70 y^{2}} - \frac{9 (14 y)}{70 y^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{9 \cdot 5 - 9 (14 y)}{70 y^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $9$ out of $9 \cdot 5 - 9 \cdot 14 y$ .

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Step 5.1.1

Factor $9$ out of $9 \cdot 5$ .

$\frac{9 (5) - 9 \cdot 14 y}{70 y^{2}}$

Step 5.1.2

Factor $9$ out of $- 9 \cdot 14 y$ .

$\frac{9 (5) + 9 (- 1 \cdot 14 y)}{70 y^{2}}$

Step 5.1.3

Factor $9$ out of $9 (5) + 9 (- 1 \cdot 14 y)$ .

$\frac{9 (5 - 1 \cdot 14 y)}{70 y^{2}}$

Step 5.2

Multiply $- 1$ by $14$ .

$\frac{9 (5 - 14 y)}{70 y^{2}}$