Solve 1/(x+h)-4-1/x-4/h

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+h-4 and x-4 is \left(x-4\right)\left(x+h-4\right). Multiply \frac{1}{x+h-4} times \frac{x-4}{x-4}. Multiply \frac{1}{x-4} times \frac{x+h-4}{x+h-4}.

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

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

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

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

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

Combine like terms in x-4-x-h+4.

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

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

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

Cancel out h in both numerator and denominator.

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

Apply the distributive property by multiplying each term of x-4 by each term of x+h-4.

$$\frac{-1}{x^{2}+xh-4x-4x-4h+16}$$

Combine -4x and -4x to get -8x.

$$\frac{-1}{x^{2}+xh-8x-4h+16}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+h-4 and x-4 is \left(x-4\right)\left(x+h-4\right). Multiply \frac{1}{x+h-4} times \frac{x-4}{x-4}. Multiply \frac{1}{x-4} times \frac{x+h-4}{x+h-4}.

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

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

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

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

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

Combine like terms in x-4-x-h+4.

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

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

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

Cancel out h in both numerator and denominator.

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

Apply the distributive property by multiplying each term of x-4 by each term of x+h-4.

$$\frac{-1}{x^{2}+xh-4x-4x-4h+16}$$

Combine -4x and -4x to get -8x.

$$\frac{-1}{x^{2}+xh-8x-4h+16}$$