Basic Math Examples

$\frac{a^{2} - 2 b^{2}}{a - b} \cdot \frac{a - b}{4} \div \frac{a + b}{16 b}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{a^{2} - 2 b^{2}}{a - b} \cdot \frac{a - b}{4} \frac{16 b}{a + b}$

Step 2

Cancel the common factor of $a - b$ .

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Step 2.1

Cancel the common factor.

$\frac{a^{2} - 2 b^{2}}{a - b} \cdot \frac{a - b}{4} \frac{16 b}{a + b}$

Step 2.2

Rewrite the expression.

$(a^{2} - 2 b^{2}) \cdot \frac{1}{4} \frac{16 b}{a + b}$

Step 3

Apply the distributive property.

$(a^{2} \frac{1}{4} - 2 b^{2} \frac{1}{4}) \frac{16 b}{a + b}$

Step 4

Combine $a^{2}$ and $\frac{1}{4}$ .

$(\frac{a^{2}}{4} - 2 b^{2} \frac{1}{4}) \frac{16 b}{a + b}$

Step 5

Cancel the common factor of $2$ .

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Step 5.1

Factor $2$ out of $- 2 b^{2}$ .

$(\frac{a^{2}}{4} + 2 (- b^{2}) \frac{1}{4}) \frac{16 b}{a + b}$

Step 5.2

Factor $2$ out of $4$ .

$(\frac{a^{2}}{4} + 2 (- b^{2}) \frac{1}{2 (2)}) \frac{16 b}{a + b}$

Step 5.3

Cancel the common factor.

$(\frac{a^{2}}{4} + 2 (- b^{2}) \frac{1}{2 \cdot 2}) \frac{16 b}{a + b}$

Step 5.4

Rewrite the expression.

$(\frac{a^{2}}{4} - b^{2} \frac{1}{2}) \frac{16 b}{a + b}$

Step 6

Combine $\frac{1}{2}$ and $b^{2}$ .

$(\frac{a^{2}}{4} - \frac{b^{2}}{2}) \frac{16 b}{a + b}$

Step 7

To write $- \frac{b^{2}}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{a^{2}}{4} - \frac{b^{2}}{2} \cdot \frac{2}{2}) \frac{16 b}{a + b}$

Step 8

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{b^{2}}{2}$ by $\frac{2}{2}$ .

$(\frac{a^{2}}{4} - \frac{b^{2} \cdot 2}{2 \cdot 2}) \frac{16 b}{a + b}$

Step 8.2

Multiply $2$ by $2$ .

$(\frac{a^{2}}{4} - \frac{b^{2} \cdot 2}{4}) \frac{16 b}{a + b}$

Step 9

Combine the numerators over the common denominator.

$\frac{a^{2} - b^{2} \cdot 2}{4} \cdot \frac{16 b}{a + b}$

Step 10

Multiply $2$ by $- 1$ .

$\frac{a^{2} - 2 b^{2}}{4} \cdot \frac{16 b}{a + b}$

Step 11

Cancel the common factor of $4$ .

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Step 11.1

Factor $4$ out of $16 b$ .

$\frac{a^{2} - 2 b^{2}}{4} \cdot \frac{4 (4 b)}{a + b}$

Step 11.2

Cancel the common factor.

$\frac{a^{2} - 2 b^{2}}{4} \cdot \frac{4 (4 b)}{a + b}$

Step 11.3

Rewrite the expression.

$(a^{2} - 2 b^{2}) \frac{4 b}{a + b}$

Step 12

Multiply $a^{2} - 2 b^{2}$ by $\frac{4 b}{a + b}$ .

$\frac{(a^{2} - 2 b^{2}) (4 b)}{a + b}$

Step 13

Simplify the expression.

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Step 13.1

Move $4$ to the left of $a^{2} - 2 b^{2}$ .

$\frac{4 \cdot (a^{2} - 2 b^{2}) b}{a + b}$

Step 13.2

Reorder factors in $\frac{4 (a^{2} - 2 b^{2}) b}{a + b}$ .

$\frac{4 b (a^{2} - 2 b^{2})}{a + b}$