Pre-Algebra Examples

$\frac{6}{17 y^{2}} - \frac{3}{5 y}$

Step 1

To write $\frac{6}{17 y^{2}}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{6}{17 y^{2}} \cdot \frac{5}{5} - \frac{3}{5 y}$

Step 2

To write $- \frac{3}{5 y}$ as a fraction with a common denominator, multiply by $\frac{17 y}{17 y}$ .

$\frac{6}{17 y^{2}} \cdot \frac{5}{5} - \frac{3}{5 y} \cdot \frac{17 y}{17 y}$

Step 3

Write each expression with a common denominator of $85 y^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{6}{17 y^{2}}$ by $\frac{5}{5}$ .

$\frac{6 \cdot 5}{17 y^{2} \cdot 5} - \frac{3}{5 y} \cdot \frac{17 y}{17 y}$

Step 3.2

Multiply $5$ by $17$ .

$\frac{6 \cdot 5}{85 y^{2}} - \frac{3}{5 y} \cdot \frac{17 y}{17 y}$

Step 3.3

Multiply $\frac{3}{5 y}$ by $\frac{17 y}{17 y}$ .

$\frac{6 \cdot 5}{85 y^{2}} - \frac{3 (17 y)}{5 y (17 y)}$

Step 3.4

Multiply $17$ by $5$ .

$\frac{6 \cdot 5}{85 y^{2}} - \frac{3 (17 y)}{85 y \cdot y}$

Step 3.5

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

$\frac{6 \cdot 5}{85 y^{2}} - \frac{3 (17 y)}{85 (y^{1} y)}$

Step 3.6

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

$\frac{6 \cdot 5}{85 y^{2}} - \frac{3 (17 y)}{85 (y^{1} y^{1})}$

Step 3.7

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

$\frac{6 \cdot 5}{85 y^{2}} - \frac{3 (17 y)}{85 y^{1 + 1}}$

Step 3.8

Add $1$ and $1$ .

$\frac{6 \cdot 5}{85 y^{2}} - \frac{3 (17 y)}{85 y^{2}}$

Step 4

Combine the numerators over the common denominator.

$\frac{6 \cdot 5 - 3 (17 y)}{85 y^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $3$ out of $6 \cdot 5 - 3 \cdot 17 y$ .

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Step 5.1.1

Factor $3$ out of $6 \cdot 5$ .

$\frac{3 (2 \cdot 5) - 3 \cdot 17 y}{85 y^{2}}$

Step 5.1.2

Factor $3$ out of $- 3 \cdot 17 y$ .

$\frac{3 (2 \cdot 5) + 3 (- 1 \cdot 17 y)}{85 y^{2}}$

Step 5.1.3

Factor $3$ out of $3 (2 \cdot 5) + 3 (- 1 \cdot 17 y)$ .

$\frac{3 (2 \cdot 5 - 1 \cdot 17 y)}{85 y^{2}}$

Step 5.2

Multiply $2$ by $5$ .

$\frac{3 (10 - 1 \cdot 17 y)}{85 y^{2}}$

Step 5.3

Multiply $- 1$ by $17$ .

$\frac{3 (10 - 17 y)}{85 y^{2}}$