Solve 1/a-1/x/frac{1{x}}

$$\frac { \frac { 1 } { a } - \frac { 1 } { x } } { \frac { 1 } { x } }$$

Evaluate

$$\frac{x}{a}-1$$

Solution Steps

Divide \frac{1}{a}-\frac{1}{x} by \frac{1}{x} by multiplying \frac{1}{a}-\frac{1}{x} by the reciprocal of \frac{1}{x}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and x is ax. Multiply \frac{1}{a} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{a}{a}.

$$\left(\frac{x}{ax}-\frac{a}{ax}\right)x$$

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

$$\frac{x-a}{ax}x$$

Express \frac{x-a}{ax}x as a single fraction.

$$\frac{\left(x-a\right)x}{ax}$$

Cancel out x in both numerator and denominator.

$$\frac{x-a}{a}$$

Expand

$$\frac{x}{a}-1$$

Solution Steps

Divide \frac{1}{a}-\frac{1}{x} by \frac{1}{x} by multiplying \frac{1}{a}-\frac{1}{x} by the reciprocal of \frac{1}{x}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of a and x is ax. Multiply \frac{1}{a} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{a}{a}.

$$\left(\frac{x}{ax}-\frac{a}{ax}\right)x$$

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

$$\frac{x-a}{ax}x$$

Express \frac{x-a}{ax}x as a single fraction.

$$\frac{\left(x-a\right)x}{ax}$$

Cancel out x in both numerator and denominator.

$$\frac{x-a}{a}$$