Algebra Examples

$\frac{\frac{1}{y^{2}} - \frac{x}{7 y^{2}}}{\frac{1}{y} - \frac{7}{x y}}$

Step 1

Multiply the numerator and denominator of the fraction by $7 x y^{2}$ .

Tap for more steps...

Step 1.1

Multiply $\frac{\frac{1}{y^{2}} - \frac{x}{7 y^{2}}}{\frac{1}{y} - \frac{7}{x y}}$ by $\frac{7 x y^{2}}{7 x y^{2}}$ .

$\frac{7 x y^{2}}{7 x y^{2}} \cdot \frac{\frac{1}{y^{2}} - \frac{x}{7 y^{2}}}{\frac{1}{y} - \frac{7}{x y}}$

Step 1.2

Combine.

$\frac{7 x y^{2} (\frac{1}{y^{2}} - \frac{x}{7 y^{2}})}{7 x y^{2} (\frac{1}{y} - \frac{7}{x y})}$

Step 2

Apply the distributive property.

$\frac{7 x y^{2} \frac{1}{y^{2}} + 7 x y^{2} (- \frac{x}{7 y^{2}})}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3

Simplify by cancelling.

Tap for more steps...

Step 3.1

Cancel the common factor of $y^{2}$ .

Tap for more steps...

Step 3.1.1

Factor $y^{2}$ out of $7 x y^{2}$ .

$\frac{y^{2} (7 x) \frac{1}{y^{2}} + 7 x y^{2} (- \frac{x}{7 y^{2}})}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.1.2

Cancel the common factor.

$\frac{y^{2} (7 x) \frac{1}{y^{2}} + 7 x y^{2} (- \frac{x}{7 y^{2}})}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.1.3

Rewrite the expression.

$\frac{7 x + 7 x y^{2} (- \frac{x}{7 y^{2}})}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.2

Cancel the common factor of $7 y^{2}$ .

Tap for more steps...

Step 3.2.1

Move the leading negative in $- \frac{x}{7 y^{2}}$ into the numerator.

$\frac{7 x + 7 x y^{2} \frac{- x}{7 y^{2}}}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.2.2

Factor $7 y^{2}$ out of $7 x y^{2}$ .

$\frac{7 x + 7 y^{2} (x) \frac{- x}{7 y^{2}}}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.2.3

Cancel the common factor.

$\frac{7 x + 7 y^{2} x \frac{- x}{7 y^{2}}}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.2.4

Rewrite the expression.

$\frac{7 x + x (- x)}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.3

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

$\frac{7 x - (x^{1} x)}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.4

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

$\frac{7 x - (x^{1} x^{1})}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.5

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

$\frac{7 x - x^{1 + 1}}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.6

Add $1$ and $1$ .

$\frac{7 x - x^{2}}{7 x y^{2} \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.7

Cancel the common factor of $y$ .

Tap for more steps...

Step 3.7.1

Factor $y$ out of $7 x y^{2}$ .

$\frac{7 x - x^{2}}{y (7 x y) \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.7.2

Cancel the common factor.

$\frac{7 x - x^{2}}{y (7 x y) \frac{1}{y} + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.7.3

Rewrite the expression.

$\frac{7 x - x^{2}}{7 x y + 7 x y^{2} (- \frac{7}{x y})}$

Step 3.8

Cancel the common factor of $x y$ .

Tap for more steps...

Step 3.8.1

Move the leading negative in $- \frac{7}{x y}$ into the numerator.

$\frac{7 x - x^{2}}{7 x y + 7 x y^{2} \frac{- 7}{x y}}$

Step 3.8.2

Factor $x y$ out of $7 x y^{2}$ .

$\frac{7 x - x^{2}}{7 x y + x y (7 y) \frac{- 7}{x y}}$

Step 3.8.3

Cancel the common factor.

$\frac{7 x - x^{2}}{7 x y + x y (7 y) \frac{- 7}{x y}}$

Step 3.8.4

Rewrite the expression.

$\frac{7 x - x^{2}}{7 x y + 7 y \cdot - 7}$

Step 3.9

Multiply $- 7$ by $7$ .

$\frac{7 x - x^{2}}{7 x y - 49 y}$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Factor $x$ out of $7 x - x^{2}$ .

Tap for more steps...

Step 4.1.1

Factor $x$ out of $7 x$ .

$\frac{x \cdot 7 - x^{2}}{7 x y - 49 y}$

Step 4.1.2

Factor $x$ out of $- x^{2}$ .

$\frac{x \cdot 7 + x (- x)}{7 x y - 49 y}$

Step 4.1.3

Factor $x$ out of $x \cdot 7 + x (- x)$ .

$\frac{x (7 - x)}{7 x y - 49 y}$

Step 4.2

Factor $7 y$ out of $7 x y - 49 y$ .

Tap for more steps...

Step 4.2.1

Factor $7 y$ out of $7 x y$ .

$\frac{x (7 - x)}{7 y (x) - 49 y}$

Step 4.2.2

Factor $7 y$ out of $- 49 y$ .

$\frac{x (7 - x)}{7 y (x) + 7 y (- 7)}$

Step 4.2.3

Factor $7 y$ out of $7 y (x) + 7 y (- 7)$ .

$\frac{x (7 - x)}{7 y (x - 7)}$

Step 4.3

Cancel the common factor of $7 - x$ and $x - 7$ .

Tap for more steps...

Step 4.3.1

Rewrite $7$ as $- 1 (- 7)$ .

$\frac{x (- 1 (- 7) - x)}{7 y (x - 7)}$

Step 4.3.2

Factor $- 1$ out of $- x$ .

$\frac{x (- 1 (- 7) - (x))}{7 y (x - 7)}$

Step 4.3.3

Factor $- 1$ out of $- 1 (- 7) - (x)$ .

$\frac{x (- 1 (- 7 + x))}{7 y (x - 7)}$

Step 4.3.4

Reorder terms.

$\frac{x (- 1 (x - 7))}{7 y (x - 7)}$

Step 4.3.5

Cancel the common factor.

$\frac{x (- 1 (x - 7))}{7 y (x - 7)}$

Step 4.3.6

Rewrite the expression.

$\frac{x \cdot (- 1)}{7 y}$

Step 4.4

Simplify the expression.

Tap for more steps...

Step 4.4.1

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{7 y}$

Step 4.4.2

Move the negative in front of the fraction.

$- \frac{x}{7 y}$