Basic Math Examples

$\frac{\frac{1}{a} + \frac{3}{3 b}}{\frac{1}{a} - \frac{5}{2 b}}$

Step 1

Cancel the common factor of $3$ .

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Step 1.1

Cancel the common factor.

$\frac{\frac{1}{a} + \frac{3}{3 b}}{\frac{1}{a} - \frac{5}{2 b}}$

Step 1.2

Rewrite the expression.

$\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{5}{2 b}}$

Step 2

Multiply the numerator and denominator of the fraction by $a b \cdot 2$ .

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Step 2.1

Multiply $\frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{5}{2 b}}$ by $\frac{a b \cdot 2}{a b \cdot 2}$ .

$\frac{a b \cdot 2}{a b \cdot 2} \cdot \frac{\frac{1}{a} + \frac{1}{b}}{\frac{1}{a} - \frac{5}{2 b}}$

Step 2.2

Combine.

$\frac{a b \cdot 2 (\frac{1}{a} + \frac{1}{b})}{a b \cdot 2 (\frac{1}{a} - \frac{5}{2 b})}$

Step 3

Apply the distributive property.

$\frac{a b \cdot 2 \frac{1}{a} + a b \cdot 2 \frac{1}{b}}{a b \cdot 2 \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4

Simplify by cancelling.

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Step 4.1

Cancel the common factor of $a$ .

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Step 4.1.1

Factor $a$ out of $a b \cdot 2$ .

$\frac{a (b \cdot 2) \frac{1}{a} + a b \cdot 2 \frac{1}{b}}{a b \cdot 2 \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.1.2

Cancel the common factor.

$\frac{a (b \cdot 2) \frac{1}{a} + a b \cdot 2 \frac{1}{b}}{a b \cdot 2 \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.1.3

Rewrite the expression.

$\frac{b \cdot 2 + a b \cdot 2 \frac{1}{b}}{a b \cdot 2 \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.2

Cancel the common factor of $b$ .

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Step 4.2.1

Factor $b$ out of $a b \cdot 2$ .

$\frac{b \cdot 2 + b (a \cdot 2) \frac{1}{b}}{a b \cdot 2 \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.2.2

Cancel the common factor.

$\frac{b \cdot 2 + b (a \cdot 2) \frac{1}{b}}{a b \cdot 2 \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.2.3

Rewrite the expression.

$\frac{b \cdot 2 + a \cdot 2}{a b \cdot 2 \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.3

Cancel the common factor of $a$ .

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Step 4.3.1

Factor $a$ out of $a b \cdot 2$ .

$\frac{b \cdot 2 + a \cdot 2}{a (b \cdot 2) \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.3.2

Cancel the common factor.

$\frac{b \cdot 2 + a \cdot 2}{a (b \cdot 2) \frac{1}{a} + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.3.3

Rewrite the expression.

$\frac{b \cdot 2 + a \cdot 2}{b \cdot 2 + a b \cdot 2 (- \frac{5}{2 b})}$

Step 4.4

Cancel the common factor of $2 b$ .

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Step 4.4.1

Move the leading negative in $- \frac{5}{2 b}$ into the numerator.

$\frac{b \cdot 2 + a \cdot 2}{b \cdot 2 + a b \cdot 2 \frac{- 5}{2 b}}$

Step 4.4.2

Factor $2 b$ out of $a b \cdot 2$ .

$\frac{b \cdot 2 + a \cdot 2}{b \cdot 2 + 2 \cdot b (a) \frac{- 5}{2 b}}$

Step 4.4.3

Cancel the common factor.

$\frac{b \cdot 2 + a \cdot 2}{b \cdot 2 + 2 \cdot b a \frac{- 5}{2 b}}$

Step 4.4.4

Rewrite the expression.

$\frac{b \cdot 2 + a \cdot 2}{b \cdot 2 + a \cdot - 5}$

Step 5

Factor $2$ out of $b \cdot 2 + a \cdot 2$ .

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Step 5.1

Factor $2$ out of $b \cdot 2$ .

$\frac{2 \cdot b + a \cdot 2}{b \cdot 2 + a \cdot - 5}$

Step 5.2

Factor $2$ out of $a \cdot 2$ .

$\frac{2 \cdot b + 2 \cdot a}{b \cdot 2 + a \cdot - 5}$

Step 5.3

Factor $2$ out of $2 \cdot b + 2 \cdot a$ .

$\frac{2 (b + a)}{b \cdot 2 + a \cdot - 5}$

Step 6

Simplify the denominator.

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Step 6.1

Move $2$ to the left of $b$ .

$\frac{2 (b + a)}{2 \cdot b + a \cdot - 5}$

Step 6.2

Move $- 5$ to the left of $a$ .

$\frac{2 (b + a)}{2 b - 5 a}$