Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

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

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

Step 3.4

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

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

Step 3.5

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

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

Step 3.6

Add $1$ and $1$ .

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

Step 3.7

Reorder the factors of $y^{2} x^{2}$ .

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

Step 4

Combine the numerators over the common denominator.

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