Solve 1/lambda+8+1/x

$$\frac { 1 } { \lambda + 8 } + \frac { 1 } { x }$$

Evaluate

$$\frac{x+\lambda +8}{x\left(\lambda +8\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \lambda +8 and x is x\left(\lambda +8\right). Multiply \frac{1}{\lambda +8} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{\lambda +8}{\lambda +8}.

$$\frac{x}{x\left(\lambda +8\right)}+\frac{\lambda +8}{x\left(\lambda +8\right)}$$

Since \frac{x}{x\left(\lambda +8\right)} and \frac{\lambda +8}{x\left(\lambda +8\right)} have the same denominator, add them by adding their numerators.

$$\frac{x+\lambda +8}{x\left(\lambda +8\right)}$$

Expand x\left(\lambda +8\right).

$$\frac{x+\lambda +8}{x\lambda +8x}$$

Differentiate w.r.t. x

$$-\frac{1}{x^{2}}$$