Solve 15/2a^2-1/3a-1+1/2a-1/4a+5-4+frac{1}{6}a

$$\frac{ 15 }{ 2 } { a }^{ 2 } - \frac{ 1 }{ 3 } a-1+ \frac{ 1 }{ 2 } a- \frac{ 1 }{ 4 } a+5-4+ \frac{ 1 }{ 6 } a$$

Evaluate

$$\frac{15a^{2}}{2}+\frac{a}{12}$$

Solution Steps

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

$$\frac{15}{2}a^{2}+\frac{1}{6}a-1-\frac{1}{4}a+5-4+\frac{1}{6}a$$

Combine \frac{1}{6}a and -\frac{1}{4}a to get -\frac{1}{12}a.

$$\frac{15}{2}a^{2}-\frac{1}{12}a-1+5-4+\frac{1}{6}a$$

Add -1 and 5 to get 4.

$$\frac{15}{2}a^{2}-\frac{1}{12}a+4-4+\frac{1}{6}a$$

Subtract 4 from 4 to get 0.

$$\frac{15}{2}a^{2}-\frac{1}{12}a+\frac{1}{6}a$$

Combine -\frac{1}{12}a and \frac{1}{6}a to get \frac{1}{12}a.

$$\frac{15}{2}a^{2}+\frac{1}{12}a$$

Factor

$$\frac{a\left(90a+1\right)}{12}$$

Solution Steps

Factor out \frac{1}{12}.

$$\frac{90a^{2}+a}{12}$$

Consider 90a^{2}-4a-12+6a-3a+60-48+2a. Multiply and combine like terms.

$$90a^{2}+a$$

Consider 90a^{2}+a. Factor out a.

$$a\left(90a+1\right)$$

Rewrite the complete factored expression.

$$\frac{a\left(90a+1\right)}{12}$$