Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Write each expression with a common denominator of $b c (b - 2)$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{a}{b}$ by $\frac{c (b - 2)}{c (b - 2)}$ .

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

Step 3.2

Multiply $\frac{2}{c (b - 2)}$ by $\frac{b}{b}$ .

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

Step 3.3

Reorder the factors of $b (c (b - 2))$ .

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

Step 3.4

Reorder the factors of $c (b - 2) b$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

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

Step 5.2

Move $- 2$ to the left of $a c$ .

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

Step 5.3

Remove parentheses.

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