Basic Math Examples

$\frac{w^{- 2} + y^{- 2}}{w^{- 1} + y^{- 1}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{1}{w^{2}} + y^{- 2}}{w^{- 1} + y^{- 1}}$

Step 1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{1}{w^{2}} + \frac{1}{y^{2}}}{w^{- 1} + y^{- 1}}$

Step 1.3

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

$\frac{\frac{1}{w^{2}} \cdot \frac{y^{2}}{y^{2}} + \frac{1}{y^{2}}}{w^{- 1} + y^{- 1}}$

Step 1.4

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

$\frac{\frac{1}{w^{2}} \cdot \frac{y^{2}}{y^{2}} + \frac{1}{y^{2}} \cdot \frac{w^{2}}{w^{2}}}{w^{- 1} + y^{- 1}}$

Step 1.5

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

Tap for more steps...

Step 1.5.1

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

$\frac{\frac{y^{2}}{w^{2} y^{2}} + \frac{1}{y^{2}} \cdot \frac{w^{2}}{w^{2}}}{w^{- 1} + y^{- 1}}$

Step 1.5.2

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

$\frac{\frac{y^{2}}{w^{2} y^{2}} + \frac{w^{2}}{y^{2} w^{2}}}{w^{- 1} + y^{- 1}}$

Step 1.5.3

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

$\frac{\frac{y^{2}}{w^{2} y^{2}} + \frac{w^{2}}{w^{2} y^{2}}}{w^{- 1} + y^{- 1}}$

Step 1.6

Combine the numerators over the common denominator.

$\frac{\frac{y^{2} + w^{2}}{w^{2} y^{2}}}{w^{- 1} + y^{- 1}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\frac{y^{2} + w^{2}}{w^{2} y^{2}}}{\frac{1}{w} + y^{- 1}}$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Write each expression with a common denominator of $w y$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 2.5.1

Multiply $\frac{1}{w}$ by $\frac{y}{y}$ .

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

Step 2.5.2

Multiply $\frac{1}{y}$ by $\frac{w}{w}$ .

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

Step 2.5.3

Reorder the factors of $y w$ .

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

Step 2.6

Combine the numerators over the common denominator.

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Cancel the common factor of $w y$ .

Tap for more steps...

Step 4.1

Factor $w y$ out of $w^{2} y^{2}$ .

$\frac{y^{2} + w^{2}}{w y (w y)} \cdot \frac{w y}{y + w}$

Step 4.2

Cancel the common factor.

$\frac{y^{2} + w^{2}}{w y (w y)} \cdot \frac{w y}{y + w}$

Step 4.3

Rewrite the expression.

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

Step 5

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

$\frac{y^{2} + w^{2}}{w y (y + w)}$