Solve (x-2)(x+1)/3-(3x-1)^2/8+(2x-3)(2x+3)/12

$$\frac { ( x - 2 ) ( x + 1 ) } { 3 } - \frac { ( 3 x - 1 ) ^ { 2 } } { 8 } + \frac { ( 2 x - 3 ) ( 2 x + 3 ) } { 12 }$$

Evaluate

$$-\frac{11x^{2}}{24}+\frac{5x}{12}-\frac{37}{24}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 8 is 24. Multiply \frac{\left(x-2\right)\left(x+1\right)}{3} times \frac{8}{8}. Multiply \frac{\left(3x-1\right)^{2}}{8} times \frac{3}{3}.

$$\frac{8\left(x-2\right)\left(x+1\right)}{24}-\frac{3\left(3x-1\right)^{2}}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

Since \frac{8\left(x-2\right)\left(x+1\right)}{24} and \frac{3\left(3x-1\right)^{2}}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\left(x-2\right)\left(x+1\right)-3\left(3x-1\right)^{2}}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

Do the multiplications in 8\left(x-2\right)\left(x+1\right)-3\left(3x-1\right)^{2}.

$$\frac{8x^{2}+8x-16x-16-27x^{2}+18x-3}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

Combine like terms in 8x^{2}+8x-16x-16-27x^{2}+18x-3.

$$\frac{-19x^{2}+10x-19}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 24 and 12 is 24. Multiply \frac{\left(2x-3\right)\left(2x+3\right)}{12} times \frac{2}{2}.

$$\frac{-19x^{2}+10x-19}{24}+\frac{2\left(2x-3\right)\left(2x+3\right)}{24}$$

Since \frac{-19x^{2}+10x-19}{24} and \frac{2\left(2x-3\right)\left(2x+3\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{-19x^{2}+10x-19+2\left(2x-3\right)\left(2x+3\right)}{24}$$

Do the multiplications in -19x^{2}+10x-19+2\left(2x-3\right)\left(2x+3\right).

$$\frac{-19x^{2}+10x-19+8x^{2}+12x-12x-18}{24}$$

Combine like terms in -19x^{2}+10x-19+8x^{2}+12x-12x-18.

$$\frac{-11x^{2}+10x-37}{24}$$

Expand

$$-\frac{11x^{2}}{24}+\frac{5x}{12}-\frac{37}{24}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 8 is 24. Multiply \frac{\left(x-2\right)\left(x+1\right)}{3} times \frac{8}{8}. Multiply \frac{\left(3x-1\right)^{2}}{8} times \frac{3}{3}.

$$\frac{8\left(x-2\right)\left(x+1\right)}{24}-\frac{3\left(3x-1\right)^{2}}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

Since \frac{8\left(x-2\right)\left(x+1\right)}{24} and \frac{3\left(3x-1\right)^{2}}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8\left(x-2\right)\left(x+1\right)-3\left(3x-1\right)^{2}}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

Do the multiplications in 8\left(x-2\right)\left(x+1\right)-3\left(3x-1\right)^{2}.

$$\frac{8x^{2}+8x-16x-16-27x^{2}+18x-3}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

Combine like terms in 8x^{2}+8x-16x-16-27x^{2}+18x-3.

$$\frac{-19x^{2}+10x-19}{24}+\frac{\left(2x-3\right)\left(2x+3\right)}{12}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 24 and 12 is 24. Multiply \frac{\left(2x-3\right)\left(2x+3\right)}{12} times \frac{2}{2}.

$$\frac{-19x^{2}+10x-19}{24}+\frac{2\left(2x-3\right)\left(2x+3\right)}{24}$$

Since \frac{-19x^{2}+10x-19}{24} and \frac{2\left(2x-3\right)\left(2x+3\right)}{24} have the same denominator, add them by adding their numerators.

$$\frac{-19x^{2}+10x-19+2\left(2x-3\right)\left(2x+3\right)}{24}$$

Do the multiplications in -19x^{2}+10x-19+2\left(2x-3\right)\left(2x+3\right).

$$\frac{-19x^{2}+10x-19+8x^{2}+12x-12x-18}{24}$$

Combine like terms in -19x^{2}+10x-19+8x^{2}+12x-12x-18.

$$\frac{-11x^{2}+10x-37}{24}$$