Solve 6+a^2+5adiv2+a=

$$6 + a ^ { 2 } + 5 a \div 2 + a =$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 6+a^{2}+a times \frac{2}{2}.

$$\frac{2\left(6+a^{2}+a\right)}{2}+\frac{5a}{2}$$

Since \frac{2\left(6+a^{2}+a\right)}{2} and \frac{5a}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\left(6+a^{2}+a\right)+5a}{2}$$

Do the multiplications in 2\left(6+a^{2}+a\right)+5a.

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

Combine like terms in 12+2a^{2}+2a+5a.

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

Factor

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

Solution Steps

Factor out \frac{1}{2}. Polynomial 2a^{2}+7a+12 is not factored since it does not have any rational roots.

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