Solve -4a+b/2+2a+3b/4-3(a-b/2-3a-b/3)

$$- \frac { 4 a + b } { 2 } + \frac { 2 a + 3 b } { 4 } - 3 ( \frac { a - b } { 2 } - \frac { 3 a - b } { 3 } )$$

Evaluate

$$\frac{3b}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply -\frac{4a+b}{2} times \frac{2}{2}.

$$-\frac{2\left(4a+b\right)}{4}+\frac{2a+3b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

Since -\frac{2\left(4a+b\right)}{4} and \frac{2a+3b}{4} have the same denominator, add them by adding their numerators.

$$\frac{-2\left(4a+b\right)+2a+3b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

Do the multiplications in -2\left(4a+b\right)+2a+3b.

$$\frac{-8a-2b+2a+3b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

Combine like terms in -8a-2b+2a+3b.

$$\frac{-6a+b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{a-b}{2} times \frac{3}{3}. Multiply \frac{3a-b}{3} times \frac{2}{2}.

$$\frac{-6a+b}{4}-3\left(\frac{3\left(a-b\right)}{6}-\frac{2\left(3a-b\right)}{6}\right)$$

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

$$\frac{-6a+b}{4}-3\times \frac{3\left(a-b\right)-2\left(3a-b\right)}{6}$$

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

$$\frac{-6a+b}{4}-3\times \frac{3a-3b-6a+2b}{6}$$

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

$$\frac{-6a+b}{4}-3\times \frac{-3a-b}{6}$$

Cancel out 6, the greatest common factor in 3 and 6.

$$\frac{-6a+b}{4}-\frac{-3a-b}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{-3a-b}{2} times \frac{2}{2}.

$$\frac{-6a+b}{4}-\frac{2\left(-3a-b\right)}{4}$$

Since \frac{-6a+b}{4} and \frac{2\left(-3a-b\right)}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-6a+b-2\left(-3a-b\right)}{4}$$

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

$$\frac{-6a+b+6a+2b}{4}$$

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

$$\frac{3b}{4}$$

Expand

$$\frac{3b}{4}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply -\frac{4a+b}{2} times \frac{2}{2}.

$$-\frac{2\left(4a+b\right)}{4}+\frac{2a+3b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

Since -\frac{2\left(4a+b\right)}{4} and \frac{2a+3b}{4} have the same denominator, add them by adding their numerators.

$$\frac{-2\left(4a+b\right)+2a+3b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

Do the multiplications in -2\left(4a+b\right)+2a+3b.

$$\frac{-8a-2b+2a+3b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

Combine like terms in -8a-2b+2a+3b.

$$\frac{-6a+b}{4}-3\left(\frac{a-b}{2}-\frac{3a-b}{3}\right)$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{a-b}{2} times \frac{3}{3}. Multiply \frac{3a-b}{3} times \frac{2}{2}.

$$\frac{-6a+b}{4}-3\left(\frac{3\left(a-b\right)}{6}-\frac{2\left(3a-b\right)}{6}\right)$$

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

$$\frac{-6a+b}{4}-3\times \frac{3\left(a-b\right)-2\left(3a-b\right)}{6}$$

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

$$\frac{-6a+b}{4}-3\times \frac{3a-3b-6a+2b}{6}$$

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

$$\frac{-6a+b}{4}-3\times \frac{-3a-b}{6}$$

Cancel out 6, the greatest common factor in 3 and 6.

$$\frac{-6a+b}{4}-\frac{-3a-b}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{-3a-b}{2} times \frac{2}{2}.

$$\frac{-6a+b}{4}-\frac{2\left(-3a-b\right)}{4}$$

Since \frac{-6a+b}{4} and \frac{2\left(-3a-b\right)}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-6a+b-2\left(-3a-b\right)}{4}$$

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

$$\frac{-6a+b+6a+2b}{4}$$

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

$$\frac{3b}{4}$$