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

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

Evaluate

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

Short Solution Steps

Cancel out x in both numerator and denominator.

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

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

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

Since \frac{3}{3x^{2}} and \frac{2x}{3x^{2}} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3x^{2} and 2x^{2} is 6x^{2}. Multiply \frac{3+2x}{3x^{2}} times \frac{2}{2}. Multiply \frac{3}{2x^{2}} times \frac{3}{3}.

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

Since \frac{2\left(3+2x\right)}{6x^{2}} and \frac{3\times 3}{6x^{2}} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{6+4x-9}{6x^{2}}$$

Combine like terms in 6+4x-9.

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

Factor

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