Basic Math Examples

$\frac{a - b}{a b} + \frac{b - c}{b c}$

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

$\frac{(a - b) c}{a b c} + \frac{(b - c) a}{b c a}$

Step 3.3

Reorder the factors of $b c a$ .

$\frac{(a - b) c}{a b c} + \frac{(b - c) a}{a b c}$

Step 4

Combine the numerators over the common denominator.

$\frac{(a - b) c + (b - c) a}{a b c}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$\frac{a c - b c + (b - c) a}{a b c}$

Step 5.2

Apply the distributive property.

$\frac{a c - b c + b a - c a}{a b c}$

Step 5.3

Subtract $c a$ from $a c$ .

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Step 5.3.1

Move $c$ .

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

Step 5.3.2

Subtract $a c$ from $a c$ .

$\frac{- b c + b a + 0}{a b c}$

Step 5.4

Add $- b c + b a$ and $0$ .

$\frac{- b c + b a}{a b c}$

Step 5.5

Rewrite $- b c + b a$ in a factored form.

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Step 5.5.1

Factor $b$ out of $- b c + b a$ .

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Step 5.5.1.1

Factor $b$ out of $- b c$ .

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

Step 5.5.1.2

Factor $b$ out of $b a$ .

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

Step 5.5.1.3

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

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

Step 5.5.2

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

$\frac{b (- c + a)}{a b c}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $b$ .

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Step 6.1.1

Cancel the common factor.

$\frac{b (- c + a)}{a b c}$

Step 6.1.2

Rewrite the expression.

$\frac{- c + a}{a c}$

Step 6.2

Factor $- 1$ out of $- c$ .

$\frac{- (c) + a}{a c}$

Step 6.3

Factor $- 1$ out of $a$ .

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

Step 6.4

Factor $- 1$ out of $- (c) - 1 (- a)$ .

$\frac{- (c - a)}{a c}$

Step 6.5

Simplify the expression.

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Step 6.5.1

Rewrite $- (c - a)$ as $- 1 (c - a)$ .

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

Step 6.5.2

Move the negative in front of the fraction.

$- \frac{c - a}{a c}$