Solve x/x^2-x-30-1/x+5

$$\frac { x } { x ^ { 2 } - x - 30 } - \frac { 1 } { x + 5 }$$

Evaluate

$$\frac{6}{\left(x-6\right)\left(x+5\right)}$$

Short Solution Steps

Factor x^{2}-x-30.

$$\frac{x}{\left(x-6\right)\left(x+5\right)}-\frac{1}{x+5}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-6\right)\left(x+5\right) and x+5 is \left(x-6\right)\left(x+5\right). Multiply \frac{1}{x+5} times \frac{x-6}{x-6}.

$$\frac{x}{\left(x-6\right)\left(x+5\right)}-\frac{x-6}{\left(x-6\right)\left(x+5\right)}$$

Since \frac{x}{\left(x-6\right)\left(x+5\right)} and \frac{x-6}{\left(x-6\right)\left(x+5\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x-\left(x-6\right)}{\left(x-6\right)\left(x+5\right)}$$

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

$$\frac{x-x+6}{\left(x-6\right)\left(x+5\right)}$$

Combine like terms in x-x+6.

$$\frac{6}{\left(x-6\right)\left(x+5\right)}$$

Expand \left(x-6\right)\left(x+5\right).

$$\frac{6}{x^{2}-x-30}$$

Differentiate w.r.t. x

$$\frac{6\left(1-2x\right)}{\left(\left(x-6\right)\left(x+5\right)\right)^{2}}$$