Solve a-2/a^2div(1-2/a)

$$\frac { a - 2 } { a ^ { 2 } } \div ( 1 - \frac { 2 } { a } )$$

Evaluate

$$\frac{1}{a}$$

Solution Steps

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

$$\frac{a-2}{a^{2}\left(1-\frac{2}{a}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$\frac{a-2}{a^{2}\left(\frac{a}{a}-\frac{2}{a}\right)}$$

Since \frac{a}{a} and \frac{2}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a-2}{a^{2}\times \frac{a-2}{a}}$$

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

$$\frac{a-2}{\frac{a^{2}\left(a-2\right)}{a}}$$

Cancel out a in both numerator and denominator.

$$\frac{a-2}{a\left(a-2\right)}$$

Cancel out a-2 in both numerator and denominator.

$$\frac{1}{a}$$

Expand

$$\frac{1}{a}$$

Solution Steps

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

$$\frac{a-2}{a^{2}\left(1-\frac{2}{a}\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{a}{a}.

$$\frac{a-2}{a^{2}\left(\frac{a}{a}-\frac{2}{a}\right)}$$

Since \frac{a}{a} and \frac{2}{a} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a-2}{a^{2}\times \frac{a-2}{a}}$$

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

$$\frac{a-2}{\frac{a^{2}\left(a-2\right)}{a}}$$

Cancel out a in both numerator and denominator.

$$\frac{a-2}{a\left(a-2\right)}$$

Cancel out a-2 in both numerator and denominator.

$$\frac{1}{a}$$