Solve 1/x-a-1/a

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{a}{a\left(x-a\right)} and \frac{x-a}{a\left(x-a\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in a-\left(x-a\right).

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

Combine like terms in a-x+a.

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

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

$$\frac{2a-x}{ax-a^{2}}$$

Differentiate w.r.t. x

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