Solve 1/x+4-1/x-7=

$$\frac { 1 } { x + 4 } - \frac { 1 } { x - 7 } =$$

Evaluate

$$-\frac{11}{\left(x-7\right)\left(x+4\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+4 and x-7 is \left(x-7\right)\left(x+4\right). Multiply \frac{1}{x+4} times \frac{x-7}{x-7}. Multiply \frac{1}{x-7} times \frac{x+4}{x+4}.

$$\frac{x-7}{\left(x-7\right)\left(x+4\right)}-\frac{x+4}{\left(x-7\right)\left(x+4\right)}$$

Since \frac{x-7}{\left(x-7\right)\left(x+4\right)} and \frac{x+4}{\left(x-7\right)\left(x+4\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-7-\left(x+4\right)}{\left(x-7\right)\left(x+4\right)}$$

Do the multiplications in x-7-\left(x+4\right).

$$\frac{x-7-x-4}{\left(x-7\right)\left(x+4\right)}$$

Combine like terms in x-7-x-4.

$$\frac{-11}{\left(x-7\right)\left(x+4\right)}$$

Expand \left(x-7\right)\left(x+4\right).

$$\frac{-11}{x^{2}-3x-28}$$

Differentiate w.r.t. x

$$\frac{11\left(2x-3\right)}{\left(\left(x-7\right)\left(x+4\right)\right)^{2}}$$