Algebra Examples

$\frac{1}{x^{2} y^{2}} + \frac{1}{x^{2} y^{3}}$

Step 1

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

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

Step 2

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

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Step 2.1

Multiply $\frac{1}{x^{2} y^{2}}$ by $\frac{y}{y}$ .

$\frac{y}{x^{2} y^{2} y} + \frac{1}{x^{2} y^{3}}$

Step 2.2

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 2.2.1

Move $y$ .

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

Step 2.2.2

Multiply $y$ by $y^{2}$ .

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

$\frac{y}{x^{2} y^{1 + 2}} + \frac{1}{x^{2} y^{3}}$

Step 2.2.3

Add $1$ and $2$ .

$\frac{y}{x^{2} y^{3}} + \frac{1}{x^{2} y^{3}}$

Step 3

Combine the numerators over the common denominator.

$\frac{y + 1}{x^{2} y^{3}}$