Basic Math Examples

$\frac{2 y + 6}{\frac{5}{\frac{y^{2 - 9}}{5 y - 15}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$(2 y + 6) \frac{\frac{y^{2 - 9}}{5 y - 15}}{5}$

Step 2

Simplify the numerator.

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Step 2.1

Subtract $9$ from $2$ .

$(2 y + 6) \frac{\frac{y^{- 7}}{5 y - 15}}{5}$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(2 y + 6) \frac{\frac{\frac{1}{y^{7}}}{5 y - 15}}{5}$

Step 3

Factor $5$ out of $5 y - 15$ .

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Step 3.1

Factor $5$ out of $5 y$ .

$(2 y + 6) \frac{\frac{\frac{1}{y^{7}}}{5 (y) - 15}}{5}$

Step 3.2

Factor $5$ out of $- 15$ .

$(2 y + 6) \frac{\frac{\frac{1}{y^{7}}}{5 y + 5 \cdot - 3}}{5}$

Step 3.3

Factor $5$ out of $5 y + 5 \cdot - 3$ .

$(2 y + 6) \frac{\frac{\frac{1}{y^{7}}}{5 (y - 3)}}{5}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$(2 y + 6) \frac{\frac{1}{y^{7}} \cdot \frac{1}{5 (y - 3)}}{5}$

Step 4.2

Combine.

$(2 y + 6) \frac{\frac{1 \cdot 1}{y^{7} (5 (y - 3))}}{5}$

Step 4.3

Multiply $1$ by $1$ .

$(2 y + 6) \frac{\frac{1}{y^{7} (5 (y - 3))}}{5}$

Step 4.4

Move $5$ to the left of $y^{7}$ .

$(2 y + 6) \frac{\frac{1}{5 y^{7} (y - 3)}}{5}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$(2 y + 6) (\frac{1}{5 y^{7} (y - 3)} \cdot \frac{1}{5})$

Step 6

Combine.

$(2 y + 6) \frac{1 \cdot 1}{5 y^{7} (y - 3) \cdot 5}$

Step 7

Multiply $1$ by $1$ .

$(2 y + 6) \frac{1}{5 y^{7} (y - 3) \cdot 5}$

Step 8

Multiply $5$ by $5$ .

$(2 y + 6) \frac{1}{25 y^{7} (y - 3)}$

Step 9

Multiply $2 y + 6$ by $\frac{1}{25 y^{7} (y - 3)}$ .

$\frac{2 y + 6}{25 y^{7} (y - 3)}$

Step 10

Factor $2$ out of $2 y + 6$ .

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Step 10.1

Factor $2$ out of $2 y$ .

$\frac{2 (y) + 6}{25 y^{7} (y - 3)}$

Step 10.2

Factor $2$ out of $6$ .

$\frac{2 y + 2 \cdot 3}{25 y^{7} (y - 3)}$

Step 10.3

Factor $2$ out of $2 y + 2 \cdot 3$ .

$\frac{2 (y + 3)}{25 y^{7} (y - 3)}$

Step 11

Apply the distributive property.

$\frac{2 y + 2 \cdot 3}{25 y^{7} (y - 3)}$

Step 12

Multiply $2$ by $3$ .

$\frac{2 y + 6}{25 y^{7} (y - 3)}$

Step 13

Split the fraction $\frac{2 y + 6}{25 y^{7} (y - 3)}$ into two fractions.

$\frac{2 y}{25 y^{7} (y - 3)} + \frac{6}{25 y^{7} (y - 3)}$

Step 14

Cancel the common factor of $y$ and $y^{7}$ .

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Step 14.1

Factor $y$ out of $2 y$ .

$\frac{y \cdot 2}{25 y^{7} (y - 3)} + \frac{6}{25 y^{7} (y - 3)}$

Step 14.2

Cancel the common factors.

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Step 14.2.1

Factor $y$ out of $25 y^{7} (y - 3)$ .

$\frac{y \cdot 2}{y (25 y^{6} (y - 3))} + \frac{6}{25 y^{7} (y - 3)}$

Step 14.2.2

Cancel the common factor.

$\frac{y \cdot 2}{y (25 y^{6} (y - 3))} + \frac{6}{25 y^{7} (y - 3)}$

Step 14.2.3

Rewrite the expression.

$\frac{2}{25 y^{6} (y - 3)} + \frac{6}{25 y^{7} (y - 3)}$