Solve x/3(x-3)-3/x(x-3)

$$\frac { x } { 3 ( x - 3 ) } - \frac { 3 } { x ( x - 3 ) }$$

Evaluate

$$\frac{1}{3}+\frac{1}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-3\right) and x\left(x-3\right) is 3x\left(x-3\right). Multiply \frac{x}{3\left(x-3\right)} times \frac{x}{x}. Multiply \frac{3}{x\left(x-3\right)} times \frac{3}{3}.

$$\frac{xx}{3x\left(x-3\right)}-\frac{3\times 3}{3x\left(x-3\right)}$$

Since \frac{xx}{3x\left(x-3\right)} and \frac{3\times 3}{3x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-3\times 3}{3x\left(x-3\right)}$$

Do the multiplications in xx-3\times 3.

$$\frac{x^{2}-9}{3x\left(x-3\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}-9}{3x\left(x-3\right)}.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{x+3}{3x}$$

Expand

$$\frac{1}{3}+\frac{1}{x}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3\left(x-3\right) and x\left(x-3\right) is 3x\left(x-3\right). Multiply \frac{x}{3\left(x-3\right)} times \frac{x}{x}. Multiply \frac{3}{x\left(x-3\right)} times \frac{3}{3}.

$$\frac{xx}{3x\left(x-3\right)}-\frac{3\times 3}{3x\left(x-3\right)}$$

Since \frac{xx}{3x\left(x-3\right)} and \frac{3\times 3}{3x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-3\times 3}{3x\left(x-3\right)}$$

Do the multiplications in xx-3\times 3.

$$\frac{x^{2}-9}{3x\left(x-3\right)}$$

Factor the expressions that are not already factored in \frac{x^{2}-9}{3x\left(x-3\right)}.

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

Cancel out x-3 in both numerator and denominator.

$$\frac{x+3}{3x}$$