Basic Math Examples

$\frac{b - \frac{1}{c}}{c - \frac{1}{b}}$

Step 1

Multiply the numerator and denominator of the fraction by $c b$ .

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Step 1.1

Multiply $\frac{b - \frac{1}{c}}{c - \frac{1}{b}}$ by $\frac{c b}{c b}$ .

$\frac{c b}{c b} \cdot \frac{b - \frac{1}{c}}{c - \frac{1}{b}}$

Step 1.2

Combine.

$\frac{c b (b - \frac{1}{c})}{c b (c - \frac{1}{b})}$

Step 2

Apply the distributive property.

$\frac{c b \cdot b + c b (- \frac{1}{c})}{c b c + c b (- \frac{1}{b})}$

Step 3

Simplify by cancelling.

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Step 3.1

Cancel the common factor of $c$ .

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Step 3.1.1

Move the leading negative in $- \frac{1}{c}$ into the numerator.

$\frac{c b \cdot b + c b \frac{- 1}{c}}{c b c + c b (- \frac{1}{b})}$

Step 3.1.2

Factor $c$ out of $c b$ .

$\frac{c b \cdot b + c (b) \frac{- 1}{c}}{c b c + c b (- \frac{1}{b})}$

Step 3.1.3

Cancel the common factor.

$\frac{c b \cdot b + c b \frac{- 1}{c}}{c b c + c b (- \frac{1}{b})}$

Step 3.1.4

Rewrite the expression.

$\frac{c b \cdot b + b \cdot - 1}{c b c + c b (- \frac{1}{b})}$

Step 3.2

Cancel the common factor of $b$ .

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Step 3.2.1

Move the leading negative in $- \frac{1}{b}$ into the numerator.

$\frac{c b \cdot b + b \cdot - 1}{c b c + c b \frac{- 1}{b}}$

Step 3.2.2

Factor $b$ out of $c b$ .

$\frac{c b \cdot b + b \cdot - 1}{c b c + b c \frac{- 1}{b}}$

Step 3.2.3

Cancel the common factor.

$\frac{c b \cdot b + b \cdot - 1}{c b c + b c \frac{- 1}{b}}$

Step 3.2.4

Rewrite the expression.

$\frac{c b \cdot b + b \cdot - 1}{c b c + c \cdot - 1}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $b$ by $b$ by adding the exponents.

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Step 4.1.1

Move $b$ .

$\frac{c (b \cdot b) + b \cdot - 1}{c b c + c \cdot - 1}$

Step 4.1.2

Multiply $b$ by $b$ .

$\frac{c b^{2} + b \cdot - 1}{c b c + c \cdot - 1}$

Step 4.2

Move $- 1$ to the left of $b$ .

$\frac{c b^{2} - 1 \cdot b}{c b c + c \cdot - 1}$

Step 4.3

Rewrite $- 1 b$ as $- b$ .

$\frac{c b^{2} - b}{c b c + c \cdot - 1}$

Step 4.4

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

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Step 4.4.1

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

$\frac{b (c b) - b}{c b c + c \cdot - 1}$

Step 4.4.2

Factor $b$ out of $- b$ .

$\frac{b (c b) + b \cdot - 1}{c b c + c \cdot - 1}$

Step 4.4.3

Factor $b$ out of $b (c b) + b \cdot - 1$ .

$\frac{b (c b - 1)}{c b c + c \cdot - 1}$

Step 5

Simplify the denominator.

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Step 5.1

Multiply $c$ by $c$ by adding the exponents.

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Step 5.1.1

Move $c$ .

$\frac{b (c b - 1)}{c \cdot c b + c \cdot - 1}$

Step 5.1.2

Multiply $c$ by $c$ .

$\frac{b (c b - 1)}{c^{2} b + c \cdot - 1}$

Step 5.2

Move $- 1$ to the left of $c$ .

$\frac{b (c b - 1)}{c^{2} b - 1 \cdot c}$

Step 5.3

Rewrite $- 1 c$ as $- c$ .

$\frac{b (c b - 1)}{c^{2} b - c}$

Step 5.4

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

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Step 5.4.1

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

$\frac{b (c b - 1)}{c (c b) - c}$

Step 5.4.2

Factor $c$ out of $- c$ .

$\frac{b (c b - 1)}{c (c b) + c \cdot - 1}$

Step 5.4.3

Factor $c$ out of $c (c b) + c \cdot - 1$ .

$\frac{b (c b - 1)}{c (c b - 1)}$

Step 6

Cancel the common factor of $c b - 1$ .

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Step 6.1

Cancel the common factor.

$\frac{b (c b - 1)}{c (c b - 1)}$

Step 6.2

Rewrite the expression.

$\frac{b}{c}$