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

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

Evaluate

$$\frac{1}{3}-\frac{4}{3x}-\frac{2}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and x^{2} is 3x^{2}. Multiply \frac{x-1}{3x} times \frac{x}{x}. Multiply \frac{x+2}{x^{2}} times \frac{3}{3}.

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

Since \frac{\left(x-1\right)x}{3x^{2}} and \frac{3\left(x+2\right)}{3x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x-1\right)x-3\left(x+2\right).

$$\frac{x^{2}-x-3x-6}{3x^{2}}$$

Combine like terms in x^{2}-x-3x-6.

$$\frac{x^{2}-4x-6}{3x^{2}}$$

Expand

$$\frac{1}{3}-\frac{4}{3x}-\frac{2}{x^{2}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x and x^{2} is 3x^{2}. Multiply \frac{x-1}{3x} times \frac{x}{x}. Multiply \frac{x+2}{x^{2}} times \frac{3}{3}.

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

Since \frac{\left(x-1\right)x}{3x^{2}} and \frac{3\left(x+2\right)}{3x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x-1\right)x-3\left(x+2\right).

$$\frac{x^{2}-x-3x-6}{3x^{2}}$$

Combine like terms in x^{2}-x-3x-6.

$$\frac{x^{2}-4x-6}{3x^{2}}$$