Solve 1/2a^2-1/3a+3/4a+2/3a^2

$$\frac { 1 } { 2 } a ^ { 2 } - \frac { 1 } { 3 } a + \frac { 3 } { 4 } a + \frac { 2 } { 3 } a ^ { 2 }$$

Evaluate

$$\frac{a\left(14a+5\right)}{12}$$

Solution Steps

Combine -\frac{1}{3}a and \frac{3}{4}a to get \frac{5}{12}a.

$$\frac{1}{2}a^{2}+\frac{5}{12}a+\frac{2}{3}a^{2}$$

Combine \frac{1}{2}a^{2} and \frac{2}{3}a^{2} to get \frac{7}{6}a^{2}.

$$\frac{7}{6}a^{2}+\frac{5}{12}a$$

Factor

$$\frac{a\left(14a+5\right)}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{6a^{2}-4a+9a+8a^{2}}{12}$$

Consider 6a^{2}-4a+9a+8a^{2}. Factor out a.

$$a\left(14a+5\right)$$

Consider 6a-4+9+8a. Multiply and combine like terms.

$$14a+5$$

Rewrite the complete factored expression.

$$\frac{a\left(14a+5\right)}{12}$$