Solve x/x-6-6/h-x=

$$\frac { x } { x - 6 } - \frac { 6 } { h - x } =$$

Evaluate

$$\frac{36-6x+hx-x^{2}}{\left(x-6\right)\left(h-x\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x-6 and h-x is \left(x-6\right)\left(-x+h\right). Multiply \frac{x}{x-6} times \frac{-x+h}{-x+h}. Multiply \frac{6}{h-x} times \frac{x-6}{x-6}.

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

Since \frac{x\left(-x+h\right)}{\left(x-6\right)\left(-x+h\right)} and \frac{6\left(x-6\right)}{\left(x-6\right)\left(-x+h\right)} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{-x^{2}+xh-6x+36}{\left(x-6\right)\left(-x+h\right)}$$

Expand \left(x-6\right)\left(-x+h\right).

$$\frac{-x^{2}+xh-6x+36}{-x^{2}+hx+6x-6h}$$

Differentiate w.r.t. x

$$\frac{6\left(-2x^{2}+2hx+12x-h^{2}-36\right)}{\left(\left(x-6\right)\left(h-x\right)\right)^{2}}$$