Solve x/x-3-x+6/x^2-3x+1/x=

$$\frac { x } { x - 3 } - \frac { x + 6 } { x ^ { 2 } - 3 x } + \frac { 1 } { x } =$$

Evaluate

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

Short Solution Steps

Factor x^{2}-3x.

$$\frac{x}{x-3}-\frac{x+6}{x\left(x-3\right)}+\frac{1}{x}$$

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

$$\frac{xx}{x\left(x-3\right)}-\frac{x+6}{x\left(x-3\right)}+\frac{1}{x}$$

Since \frac{xx}{x\left(x-3\right)} and \frac{x+6}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-\left(x+6\right)}{x\left(x-3\right)}+\frac{1}{x}$$

Do the multiplications in xx-\left(x+6\right).

$$\frac{x^{2}-x-6}{x\left(x-3\right)}+\frac{1}{x}$$

Factor the expressions that are not already factored in \frac{x^{2}-x-6}{x\left(x-3\right)}.

$$\frac{\left(x-3\right)\left(x+2\right)}{x\left(x-3\right)}+\frac{1}{x}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x+2}{x}+\frac{1}{x}$$

Since \frac{x+2}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{x+2+1}{x}$$

Combine like terms in x+2+1.

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

Expand

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

Short Solution Steps

Factor x^{2}-3x.

$$\frac{x}{x-3}-\frac{x+6}{x\left(x-3\right)}+\frac{1}{x}$$

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

$$\frac{xx}{x\left(x-3\right)}-\frac{x+6}{x\left(x-3\right)}+\frac{1}{x}$$

Since \frac{xx}{x\left(x-3\right)} and \frac{x+6}{x\left(x-3\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{xx-\left(x+6\right)}{x\left(x-3\right)}+\frac{1}{x}$$

Do the multiplications in xx-\left(x+6\right).

$$\frac{x^{2}-x-6}{x\left(x-3\right)}+\frac{1}{x}$$

Factor the expressions that are not already factored in \frac{x^{2}-x-6}{x\left(x-3\right)}.

$$\frac{\left(x-3\right)\left(x+2\right)}{x\left(x-3\right)}+\frac{1}{x}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x+2}{x}+\frac{1}{x}$$

Since \frac{x+2}{x} and \frac{1}{x} have the same denominator, add them by adding their numerators.

$$\frac{x+2+1}{x}$$

Combine like terms in x+2+1.

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