Solve -2ab/2+3ba-3x/2+ab=

$$- \frac { 2 a b } { 2 } + 3 b a - \frac { 3 x } { 2 } + a b =$$

Evaluate

$$3ab-\frac{3x}{2}$$

Short Solution Steps

Cancel out 2 and 2.

$$-ab+3ba-\frac{3x}{2}+ab$$

Combine 3ba and ab to get 4ba.

$$-ab+4ba-\frac{3x}{2}$$

Combine -ab and 4ba to get 3ab.

$$3ab-\frac{3x}{2}$$

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

$$\frac{2\times 3ab}{2}-\frac{3x}{2}$$

Since \frac{2\times 3ab}{2} and \frac{3x}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\times 3ab-3x}{2}$$

Do the multiplications in 2\times 3ab-3x.

$$\frac{6ab-3x}{2}$$

Factor

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

Solution Steps

Factor out \frac{1}{2}.

$$\frac{-2ab+6ba-3x+2ab}{2}$$

Consider -2ab+6ba-3x+2ab. Multiply and combine like terms.

$$-3x+6ab$$

Consider -3x+6ab. Factor out 3.

$$3\left(-x+2ab\right)$$

Rewrite the complete factored expression.

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