Solve x/5{frac{5/x^2}}

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

Evaluate

$$\frac{1}{x}$$

Solution Steps

Divide x by \frac{5}{\frac{5}{x^{2}}} by multiplying x by the reciprocal of \frac{5}{\frac{5}{x^{2}}}.

$$\frac{x\times \frac{5}{x^{2}}}{5}$$

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

$$\frac{\frac{x\times 5}{x^{2}}}{5}$$

Cancel out x in both numerator and denominator.

$$\frac{\frac{5}{x}}{5}$$

Express \frac{\frac{5}{x}}{5} as a single fraction.

$$\frac{5}{x\times 5}$$

Differentiate w.r.t. x

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