Solve x+5quad1/x^2-5x

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

Evaluate

$$\frac{x^{3}-5x^{2}+5}{x\left(x-5\right)}$$

Short Solution Steps

Express 5\times \frac{1}{x^{2}-5x} as a single fraction.

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

Factor x^{2}-5x.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{x\left(x-5\right)}{x\left(x-5\right)}.

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

Since \frac{xx\left(x-5\right)}{x\left(x-5\right)} and \frac{5}{x\left(x-5\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in xx\left(x-5\right)+5.

$$\frac{x^{3}-5x^{2}+5}{x\left(x-5\right)}$$

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

$$\frac{x^{3}-5x^{2}+5}{x^{2}-5x}$$

Differentiate w.r.t. x

$$\frac{x^{4}-10x^{3}+25x^{2}-10x+25}{\left(x\left(x-5\right)\right)^{2}}$$