Solve (x+2)(x-3)/2-(2x-1)(x+1)/3

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

Evaluate

$$-\frac{x^{2}}{6}-\frac{5x}{6}-\frac{8}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{\left(x+2\right)\left(x-3\right)}{2} times \frac{3}{3}. Multiply \frac{\left(2x-1\right)\left(x+1\right)}{3} times \frac{2}{2}.

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

Since \frac{3\left(x+2\right)\left(x-3\right)}{6} and \frac{2\left(2x-1\right)\left(x+1\right)}{6} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{3x^{2}-9x+6x-18-4x^{2}-4x+2x+2}{6}$$

Combine like terms in 3x^{2}-9x+6x-18-4x^{2}-4x+2x+2.

$$\frac{-x^{2}-5x-16}{6}$$

Expand

$$-\frac{x^{2}}{6}-\frac{5x}{6}-\frac{8}{3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{\left(x+2\right)\left(x-3\right)}{2} times \frac{3}{3}. Multiply \frac{\left(2x-1\right)\left(x+1\right)}{3} times \frac{2}{2}.

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

Since \frac{3\left(x+2\right)\left(x-3\right)}{6} and \frac{2\left(2x-1\right)\left(x+1\right)}{6} have the same denominator, subtract them by subtracting their numerators.

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

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

$$\frac{3x^{2}-9x+6x-18-4x^{2}-4x+2x+2}{6}$$

Combine like terms in 3x^{2}-9x+6x-18-4x^{2}-4x+2x+2.

$$\frac{-x^{2}-5x-16}{6}$$