Solve (x-4/x+8(x+h))-(x-4/x+8)/h

$$\frac { ( \frac { x - 4 } { x + 8 } ( x + h ) ) - ( \frac { x - 4 } { x + 8 } ) } { h }$$

Evaluate

$$\frac{\left(x-4\right)\left(x+h-1\right)}{h\left(x+8\right)}$$

Short Solution Steps

Express \frac{x-4}{x+8}\left(x+h\right) as a single fraction.

$$\frac{\frac{\left(x-4\right)\left(x+h\right)}{x+8}-\frac{x-4}{x+8}}{h}$$

Since \frac{\left(x-4\right)\left(x+h\right)}{x+8} and \frac{x-4}{x+8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-4\right)\left(x+h\right)-\left(x-4\right)}{x+8}}{h}$$

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

$$\frac{\frac{x^{2}+xh-4x-4h-x+4}{x+8}}{h}$$

Combine like terms in x^{2}+xh-4x-4h-x+4.

$$\frac{\frac{x^{2}+xh-5x-4h+4}{x+8}}{h}$$

Express \frac{\frac{x^{2}+xh-5x-4h+4}{x+8}}{h} as a single fraction.

$$\frac{x^{2}+xh-5x-4h+4}{\left(x+8\right)h}$$

Use the distributive property to multiply x+8 by h.

$$\frac{x^{2}+xh-5x-4h+4}{xh+8h}$$

Expand

$$\frac{x^{2}+hx-5x-4h+4}{h\left(x+8\right)}$$

Short Solution Steps

Express \frac{x-4}{x+8}\left(x+h\right) as a single fraction.

$$\frac{\frac{\left(x-4\right)\left(x+h\right)}{x+8}-\frac{x-4}{x+8}}{h}$$

Since \frac{\left(x-4\right)\left(x+h\right)}{x+8} and \frac{x-4}{x+8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{\left(x-4\right)\left(x+h\right)-\left(x-4\right)}{x+8}}{h}$$

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

$$\frac{\frac{x^{2}+xh-4x-4h-x+4}{x+8}}{h}$$

Combine like terms in x^{2}+xh-4x-4h-x+4.

$$\frac{\frac{x^{2}+xh-5x-4h+4}{x+8}}{h}$$

Express \frac{\frac{x^{2}+xh-5x-4h+4}{x+8}}{h} as a single fraction.

$$\frac{x^{2}+xh-5x-4h+4}{\left(x+8\right)h}$$

Use the distributive property to multiply x+8 by h.

$$\frac{x^{2}+xh-5x-4h+4}{xh+8h}$$