Algebra Examples

$\frac{5}{2 a^{2} b} + \frac{3}{6 a b^{2}}$

Step 1

Cancel the common factor of $3$ and $6$ .

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Step 1.1

Factor $3$ out of $3$ .

$\frac{5}{2 a^{2} b} + \frac{3 (1)}{6 a b^{2}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $3$ out of $6 a b^{2}$ .

$\frac{5}{2 a^{2} b} + \frac{3 (1)}{3 (2 a b^{2})}$

Step 1.2.2

Cancel the common factor.

$\frac{5}{2 a^{2} b} + \frac{3 \cdot 1}{3 (2 a b^{2})}$

Step 1.2.3

Rewrite the expression.

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

Step 2

To write $\frac{5}{2 a^{2} b}$ as a fraction with a common denominator, multiply by $\frac{b}{b}$ .

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

Step 3

To write $\frac{1}{2 a b^{2}}$ as a fraction with a common denominator, multiply by $\frac{a}{a}$ .

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

Step 4

Write each expression with a common denominator of $2 a^{2} b^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{5}{2 a^{2} b}$ by $\frac{b}{b}$ .

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

Step 4.2

Raise $b$ to the power of $1$ .

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

Step 4.3

Raise $b$ to the power of $1$ .

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

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 4.5

Add $1$ and $1$ .

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

Step 4.6

Multiply $\frac{1}{2 a b^{2}}$ by $\frac{a}{a}$ .

$\frac{5 b}{2 a^{2} b^{2}} + \frac{a}{2 a b^{2} a}$

Step 4.7

Raise $a$ to the power of $1$ .

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

Step 4.8

Raise $a$ to the power of $1$ .

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

Step 4.9

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 4.10

Add $1$ and $1$ .

$\frac{5 b}{2 a^{2} b^{2}} + \frac{a}{2 a^{2} b^{2}}$

Step 5

Combine the numerators over the common denominator.

$\frac{5 b + a}{2 a^{2} b^{2}}$