Solve k^2-3kh/k^2-h^2*(k+h)^2/4k-12h

$$\frac { k ^ { 2 } - 3 k h } { k ^ { 2 } - h ^ { 2 } } \times \frac { ( k + h ) ^ { 2 } } { 4 k - 12 h }$$

Evaluate

$$\frac{k\left(h+k\right)}{4\left(k-h\right)}$$

Short Solution Steps

Multiply \frac{k^{2}-3kh}{k^{2}-h^{2}} times \frac{\left(k+h\right)^{2}}{4k-12h} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(k^{2}-3kh\right)\left(k+h\right)^{2}}{\left(k^{2}-h^{2}\right)\left(4k-12h\right)}$$

Factor the expressions that are not already factored.

$$\frac{k\left(-3h+k\right)\left(h+k\right)^{2}}{4\left(h+k\right)\left(-3h+k\right)\left(-h+k\right)}$$

Cancel out \left(h+k\right)\left(-3h+k\right) in both numerator and denominator.

$$\frac{k\left(h+k\right)}{4\left(-h+k\right)}$$

Expand the expression.

$$\frac{hk+k^{2}}{-4h+4k}$$

Expand

$$\frac{hk+k^{2}}{4\left(k-h\right)}$$

Short Solution Steps

Multiply \frac{k^{2}-3kh}{k^{2}-h^{2}} times \frac{\left(k+h\right)^{2}}{4k-12h} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(k^{2}-3kh\right)\left(k+h\right)^{2}}{\left(k^{2}-h^{2}\right)\left(4k-12h\right)}$$

Factor the expressions that are not already factored.

$$\frac{k\left(-3h+k\right)\left(h+k\right)^{2}}{4\left(h+k\right)\left(-3h+k\right)\left(-h+k\right)}$$

Cancel out \left(h+k\right)\left(-3h+k\right) in both numerator and denominator.

$$\frac{k\left(h+k\right)}{4\left(-h+k\right)}$$

Expand the expression.

$$\frac{hk+k^{2}}{-4h+4k}$$