Algebra Examples

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{8}{24 a b^{3}}$

Step 1

Cancel the common factor of $8$ and $24$ .

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Step 1.1

Factor $8$ out of $8$ .

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{8 (1)}{24 a b^{3}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $8$ out of $24 a b^{3}$ .

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{8 (1)}{8 (3 a b^{3})}$

Step 1.2.2

Cancel the common factor.

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{8 \cdot 1}{8 (3 a b^{3})}$

Step 1.2.3

Rewrite the expression.

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{1}{3 a b^{3}}$

Step 2

To write $\frac{1}{3 a b^{3}}$ as a fraction with a common denominator, multiply by $\frac{5 a}{5 a}$ .

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{1}{3 a b^{3}} \cdot \frac{5 a}{5 a}$

Step 3

Write each expression with a common denominator of $15 a^{2} b^{3}$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{1}{3 a b^{3}}$ by $\frac{5 a}{5 a}$ .

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{5 a}{3 a b^{3} (5 a)}$

Step 3.2

Multiply $5$ by $3$ .

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{5 a}{15 a b^{3} a}$

Step 3.3

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

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{5 a}{15 (a^{1} a) b^{3}}$

Step 3.4

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

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{5 a}{15 (a^{1} a^{1}) b^{3}}$

Step 3.5

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

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{5 a}{15 a^{1 + 1} b^{3}}$

Step 3.6

Add $1$ and $1$ .

$\frac{a - 5}{15 a^{2} b^{3}} + \frac{5 a}{15 a^{2} b^{3}}$

Step 4

Combine the numerators over the common denominator.

$\frac{a - 5 + 5 a}{15 a^{2} b^{3}}$

Step 5

Add $a$ and $5 a$ .

$\frac{6 a - 5}{15 a^{2} b^{3}}$