Solve (a-b)*3/2+2*(a-3)/2+(a-2)*(a-3)/2=

$$\frac { ( a - b ) \cdot 3 } { 2 } + \frac { 2 \cdot ( a - 3 ) } { 2 } + \frac { ( a - 2 ) \cdot ( a - 3 ) } { 2 } =$$

Evaluate

$$\frac{a^{2}-3b}{2}$$

Short Solution Steps

Cancel out 2 and 2.

$$\frac{\left(a-b\right)\times 3}{2}+a-3+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a-3 times \frac{2}{2}.

$$\frac{\left(a-b\right)\times 3}{2}+\frac{2\left(a-3\right)}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

Since \frac{\left(a-b\right)\times 3}{2} and \frac{2\left(a-3\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(a-b\right)\times 3+2\left(a-3\right)}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

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

$$\frac{3a-3b+2a-6}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

Combine like terms in 3a-3b+2a-6.

$$\frac{5a-3b-6}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

Since \frac{5a-3b-6}{2} and \frac{\left(a-2\right)\left(a-3\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{5a-3b-6+\left(a-2\right)\left(a-3\right)}{2}$$

Do the multiplications in 5a-3b-6+\left(a-2\right)\left(a-3\right).

$$\frac{5a-3b-6+a^{2}-3a-2a+6}{2}$$

Combine like terms in 5a-3b-6+a^{2}-3a-2a+6.

$$\frac{-3b+a^{2}}{2}$$

Expand

$$\frac{a^{2}-3b}{2}$$

Short Solution Steps

Cancel out 2 and 2.

$$\frac{\left(a-b\right)\times 3}{2}+a-3+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply a-3 times \frac{2}{2}.

$$\frac{\left(a-b\right)\times 3}{2}+\frac{2\left(a-3\right)}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

Since \frac{\left(a-b\right)\times 3}{2} and \frac{2\left(a-3\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(a-b\right)\times 3+2\left(a-3\right)}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

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

$$\frac{3a-3b+2a-6}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

Combine like terms in 3a-3b+2a-6.

$$\frac{5a-3b-6}{2}+\frac{\left(a-2\right)\left(a-3\right)}{2}$$

Since \frac{5a-3b-6}{2} and \frac{\left(a-2\right)\left(a-3\right)}{2} have the same denominator, add them by adding their numerators.

$$\frac{5a-3b-6+\left(a-2\right)\left(a-3\right)}{2}$$

Do the multiplications in 5a-3b-6+\left(a-2\right)\left(a-3\right).

$$\frac{5a-3b-6+a^{2}-3a-2a+6}{2}$$

Combine like terms in 5a-3b-6+a^{2}-3a-2a+6.

$$\frac{-3b+a^{2}}{2}$$