Solve 4(x-3)/3:2(x-1)-2x+3/2

$$\frac { 4 ( x - 3 ) } { 3 } : 2 ( x - 1 ) - \frac { 2 x + 3 } { 2 }$$

Evaluate

$$\frac{2x^{2}}{3}-\frac{11x}{3}+\frac{1}{2}$$

Short Solution Steps

Express \frac{\frac{4\left(x-3\right)}{3}}{2} as a single fraction.

$$\frac{4\left(x-3\right)}{3\times 2}\left(x-1\right)-\frac{2x+3}{2}$$

Cancel out 2 in both numerator and denominator.

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

Express \frac{2\left(x-3\right)}{3}\left(x-1\right) as a single fraction.

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

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

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

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

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

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

$$\frac{4x^{2}-4x-12x+12-6x-9}{6}$$

Combine like terms in 4x^{2}-4x-12x+12-6x-9.

$$\frac{4x^{2}-22x+3}{6}$$

Expand

$$\frac{2x^{2}}{3}-\frac{11x}{3}+\frac{1}{2}$$

Short Solution Steps

Express \frac{\frac{4\left(x-3\right)}{3}}{2} as a single fraction.

$$\frac{4\left(x-3\right)}{3\times 2}\left(x-1\right)-\frac{2x+3}{2}$$

Cancel out 2 in both numerator and denominator.

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

Express \frac{2\left(x-3\right)}{3}\left(x-1\right) as a single fraction.

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

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

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

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

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

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

$$\frac{4x^{2}-4x-12x+12-6x-9}{6}$$

Combine like terms in 4x^{2}-4x-12x+12-6x-9.

$$\frac{4x^{2}-22x+3}{6}$$