Solve x^2-4x-32/xy-8y-(x-3y)^2-9y^2/xy

$$\frac { x ^ { 2 } - 4 x - 32 } { x y - 8 y } - \frac { ( x - 3 y ) ^ { 2 } - 9 y ^ { 2 } } { x y }$$

Evaluate

$$6+\frac{4}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4x-32}{xy-8y}.

$$\frac{\left(x-8\right)\left(x+4\right)}{y\left(x-8\right)}-\frac{\left(x-3y\right)^{2}-9y^{2}}{xy}$$

Cancel out x-8 in both numerator and denominator.

$$\frac{x+4}{y}-\frac{\left(x-3y\right)^{2}-9y^{2}}{xy}$$

Factor the expressions that are not already factored in \frac{\left(x-3y\right)^{2}-9y^{2}}{xy}.

$$\frac{x+4}{y}-\frac{x\left(x-6y\right)}{xy}$$

Cancel out x in both numerator and denominator.

$$\frac{x+4}{y}-\frac{x-6y}{y}$$

Since \frac{x+4}{y} and \frac{x-6y}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+4-\left(x-6y\right)}{y}$$

Do the multiplications in x+4-\left(x-6y\right).

$$\frac{x+4-x+6y}{y}$$

Combine like terms in x+4-x+6y.

$$\frac{4+6y}{y}$$

Expand

$$6+\frac{4}{y}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-4x-32}{xy-8y}.

$$\frac{\left(x-8\right)\left(x+4\right)}{y\left(x-8\right)}-\frac{\left(x-3y\right)^{2}-9y^{2}}{xy}$$

Cancel out x-8 in both numerator and denominator.

$$\frac{x+4}{y}-\frac{\left(x-3y\right)^{2}-9y^{2}}{xy}$$

Factor the expressions that are not already factored in \frac{\left(x-3y\right)^{2}-9y^{2}}{xy}.

$$\frac{x+4}{y}-\frac{x\left(x-6y\right)}{xy}$$

Cancel out x in both numerator and denominator.

$$\frac{x+4}{y}-\frac{x-6y}{y}$$

Since \frac{x+4}{y} and \frac{x-6y}{y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x+4-\left(x-6y\right)}{y}$$

Do the multiplications in x+4-\left(x-6y\right).

$$\frac{x+4-x+6y}{y}$$

Combine like terms in x+4-x+6y.

$$\frac{4+6y}{y}$$