Algebra Examples

$\frac{1}{5 y^{4}} + \frac{2}{y^{3}}$

Step 1

To write $\frac{2}{y^{3}}$ as a fraction with a common denominator, multiply by $\frac{5 y}{5 y}$ .

$\frac{1}{5 y^{4}} + \frac{2}{y^{3}} \cdot \frac{5 y}{5 y}$

Step 2

Write each expression with a common denominator of $5 y^{4}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1

Multiply $\frac{2}{y^{3}}$ by $\frac{5 y}{5 y}$ .

$\frac{1}{5 y^{4}} + \frac{2 (5 y)}{y^{3} (5 y)}$

Step 2.2

Multiply $y^{3}$ by $y$ by adding the exponents.

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Step 2.2.1

Move $y$ .

$\frac{1}{5 y^{4}} + \frac{2 (5 y)}{y \cdot y^{3} \cdot 5}$

Step 2.2.2

Multiply $y$ by $y^{3}$ .

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Step 2.2.2.1

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

$\frac{1}{5 y^{4}} + \frac{2 (5 y)}{y^{1} y^{3} \cdot 5}$

Step 2.2.2.2

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

$\frac{1}{5 y^{4}} + \frac{2 (5 y)}{y^{1 + 3} \cdot 5}$

Step 2.2.3

Add $1$ and $3$ .

$\frac{1}{5 y^{4}} + \frac{2 (5 y)}{y^{4} \cdot 5}$

Step 2.3

Reorder the factors of $y^{4} \cdot 5$ .

$\frac{1}{5 y^{4}} + \frac{2 (5 y)}{5 y^{4}}$

Step 3

Combine the numerators over the common denominator.

$\frac{1 + 2 (5 y)}{5 y^{4}}$

Step 4

Multiply $2$ by $5$ .

$\frac{1 + 10 y}{5 y^{4}}$