Solve a^2-y^2/ay-y^2-2a/a-y

$$\frac { a ^ { 2 } - y ^ { 2 } } { a y - y ^ { 2 } } - \frac { 2 a } { a - y }$$

Evaluate

$$\frac{a^{2}-2ay-y^{2}}{y\left(a-y\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-y^{2}}{ay-y^{2}}.

$$\frac{\left(y+a\right)\left(-y+a\right)}{y\left(-y+a\right)}-\frac{2a}{a-y}$$

Cancel out -y+a in both numerator and denominator.

$$\frac{y+a}{y}-\frac{2a}{a-y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and a-y is y\left(-y+a\right). Multiply \frac{y+a}{y} times \frac{-y+a}{-y+a}. Multiply \frac{2a}{a-y} times \frac{y}{y}.

$$\frac{\left(y+a\right)\left(-y+a\right)}{y\left(-y+a\right)}-\frac{2ay}{y\left(-y+a\right)}$$

Since \frac{\left(y+a\right)\left(-y+a\right)}{y\left(-y+a\right)} and \frac{2ay}{y\left(-y+a\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(y+a\right)\left(-y+a\right)-2ay}{y\left(-y+a\right)}$$

Do the multiplications in \left(y+a\right)\left(-y+a\right)-2ay.

$$\frac{ay-y^{2}-ay+a^{2}-2ay}{y\left(-y+a\right)}$$

Combine like terms in ay-y^{2}-ay+a^{2}-2ay.

$$\frac{-y^{2}-2ay+a^{2}}{y\left(-y+a\right)}$$

Expand y\left(-y+a\right).

$$\frac{-y^{2}-2ay+a^{2}}{-y^{2}+ay}$$

Expand

$$-\frac{y^{2}+2ay-a^{2}}{y\left(a-y\right)}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{a^{2}-y^{2}}{ay-y^{2}}.

$$\frac{\left(y+a\right)\left(-y+a\right)}{y\left(-y+a\right)}-\frac{2a}{a-y}$$

Cancel out -y+a in both numerator and denominator.

$$\frac{y+a}{y}-\frac{2a}{a-y}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of y and a-y is y\left(-y+a\right). Multiply \frac{y+a}{y} times \frac{-y+a}{-y+a}. Multiply \frac{2a}{a-y} times \frac{y}{y}.

$$\frac{\left(y+a\right)\left(-y+a\right)}{y\left(-y+a\right)}-\frac{2ay}{y\left(-y+a\right)}$$

Since \frac{\left(y+a\right)\left(-y+a\right)}{y\left(-y+a\right)} and \frac{2ay}{y\left(-y+a\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(y+a\right)\left(-y+a\right)-2ay}{y\left(-y+a\right)}$$

Do the multiplications in \left(y+a\right)\left(-y+a\right)-2ay.

$$\frac{ay-y^{2}-ay+a^{2}-2ay}{y\left(-y+a\right)}$$

Combine like terms in ay-y^{2}-ay+a^{2}-2ay.

$$\frac{-y^{2}-2ay+a^{2}}{y\left(-y+a\right)}$$

Expand y\left(-y+a\right).

$$\frac{-y^{2}-2ay+a^{2}}{-y^{2}+ay}$$