Simplify ((x^2)/(y^2)-1)/(x/y+1)

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

Step 1

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

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

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

Combine.

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

Step 2

Apply the distributive property.

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

Step 3

Simplify by cancelling.

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Simplify the numerator.

Move $- 1$ to the left of $y^{2}$ .

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

Rewrite $- 1 y^{2}$ as $- y^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = y$ .

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

Step 5

Simplify the denominator.

Factor $y$ out of $y x + y^{2} \cdot 1$ .

Factor $y$ out of $y x$ .

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

Factor $y$ out of $y^{2} \cdot 1$ .

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

Factor $y$ out of $y (x) + y (y \cdot 1)$ .

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

Multiply $y$ by $1$ .

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

Step 6

Cancel the common factor of $x + y$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((x^2)/(y^2)-1)/(x/y+1)

Related Questions

Support LCMGCF.com by disabling your adblocker.