Solve -[3/2ab-1/30ab+(3/5ab-1/3ab+frac{1}{6}ab-frac{5}{2}ab)]-[(frac{3}{2}a+frac{5}{3}a-frac{1}{6}a)+(frac{2}{9}a-frac{1}{3}a)]

$$- [ \frac { 3 } { 2 } a b - \frac { 1 } { 30 } a b + ( \frac { 3 } { 5 } a b - \frac { 1 } { 3 } a b + \frac { 1 } { 6 } a b - \frac { 5 } { 2 } a b ) ] - [ ( \frac { 3 } { 2 } a + \frac { 5 } { 3 } a - \frac { 1 } { 6 } a ) + ( \frac { 2 } { 9 } a - \frac { 1 } { 3 } a ) ]$$

Evaluate

$$\frac{3ab}{5}-\frac{26a}{9}$$

Solution Steps

Combine \frac{3}{2}ab and -\frac{1}{30}ab to get \frac{22}{15}ab.

$$-\left(\frac{22}{15}ab+\frac{3}{5}ab-\frac{1}{3}ab+\frac{1}{6}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{22}{15}ab and \frac{3}{5}ab to get \frac{31}{15}ab.

$$-\left(\frac{31}{15}ab-\frac{1}{3}ab+\frac{1}{6}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{31}{15}ab and -\frac{1}{3}ab to get \frac{26}{15}ab.

$$-\left(\frac{26}{15}ab+\frac{1}{6}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{26}{15}ab and \frac{1}{6}ab to get \frac{19}{10}ab.

$$-\left(\frac{19}{10}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{19}{10}ab and -\frac{5}{2}ab to get -\frac{3}{5}ab.

$$-\left(-\frac{3}{5}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

The opposite of -\frac{3}{5}ab is \frac{3}{5}ab.

$$\frac{3}{5}ab-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{3}{2}a and \frac{5}{3}a to get \frac{19}{6}a.

$$\frac{3}{5}ab-\left(\frac{19}{6}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{19}{6}a and -\frac{1}{6}a to get 3a.

$$\frac{3}{5}ab-\left(3a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine 3a and \frac{2}{9}a to get \frac{29}{9}a.

$$\frac{3}{5}ab-\left(\frac{29}{9}a-\frac{1}{3}a\right)$$

Combine \frac{29}{9}a and -\frac{1}{3}a to get \frac{26}{9}a.

$$\frac{3}{5}ab-\frac{26}{9}a$$

Expand

$$\frac{3ab}{5}-\frac{26a}{9}$$

Solution Steps

Combine \frac{3}{2}ab and -\frac{1}{30}ab to get \frac{22}{15}ab.

$$-\left(\frac{22}{15}ab+\frac{3}{5}ab-\frac{1}{3}ab+\frac{1}{6}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{22}{15}ab and \frac{3}{5}ab to get \frac{31}{15}ab.

$$-\left(\frac{31}{15}ab-\frac{1}{3}ab+\frac{1}{6}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{31}{15}ab and -\frac{1}{3}ab to get \frac{26}{15}ab.

$$-\left(\frac{26}{15}ab+\frac{1}{6}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{26}{15}ab and \frac{1}{6}ab to get \frac{19}{10}ab.

$$-\left(\frac{19}{10}ab-\frac{5}{2}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{19}{10}ab and -\frac{5}{2}ab to get -\frac{3}{5}ab.

$$-\left(-\frac{3}{5}ab\right)-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

The opposite of -\frac{3}{5}ab is \frac{3}{5}ab.

$$\frac{3}{5}ab-\left(\frac{3}{2}a+\frac{5}{3}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{3}{2}a and \frac{5}{3}a to get \frac{19}{6}a.

$$\frac{3}{5}ab-\left(\frac{19}{6}a-\frac{1}{6}a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine \frac{19}{6}a and -\frac{1}{6}a to get 3a.

$$\frac{3}{5}ab-\left(3a+\frac{2}{9}a-\frac{1}{3}a\right)$$

Combine 3a and \frac{2}{9}a to get \frac{29}{9}a.

$$\frac{3}{5}ab-\left(\frac{29}{9}a-\frac{1}{3}a\right)$$

Combine \frac{29}{9}a and -\frac{1}{3}a to get \frac{26}{9}a.

$$\frac{3}{5}ab-\frac{26}{9}a$$