Solve 5/6ab-1/2a+2ab-1/3a+1/2a-ab

$$\frac { 5 } { 6 } a b - \frac { 1 } { 2 } a + 2 a b - \frac { 1 } { 3 } a + \frac { 1 } { 2 } a - a b$$

Evaluate

$$\frac{11ab}{6}-\frac{a}{3}$$

Solution Steps

Combine \frac{5}{6}ab and 2ab to get \frac{17}{6}ab.

$$\frac{17}{6}ab-\frac{1}{2}a-\frac{1}{3}a+\frac{1}{2}a-ab$$

Combine -\frac{1}{2}a and -\frac{1}{3}a to get -\frac{5}{6}a.

$$\frac{17}{6}ab-\frac{5}{6}a+\frac{1}{2}a-ab$$

Combine -\frac{5}{6}a and \frac{1}{2}a to get -\frac{1}{3}a.

$$\frac{17}{6}ab-\frac{1}{3}a-ab$$

Combine \frac{17}{6}ab and -ab to get \frac{11}{6}ab.

$$\frac{11}{6}ab-\frac{1}{3}a$$

Factor

$$\frac{a\left(11b-2\right)}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{5ab-3a+12ab-2a+3a-6ab}{6}$$

Consider 5ab-3a+12ab-2a+3a-6ab. Factor out a.

$$a\left(11b-2\right)$$

Consider 5b-3+12b-2+3-6b. Multiply and combine like terms.

$$11b-2$$

Rewrite the complete factored expression.

$$\frac{a\left(11b-2\right)}{6}$$