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

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

Evaluate

$$\frac{3x^{2}}{2}-\frac{x}{6}+\frac{5}{4}$$

Solution Steps

Combine \frac{1}{2}x^{2} and x^{2} to get \frac{3}{2}x^{2}.

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

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

$$\frac{3}{2}x^{2}-\frac{1}{6}x+2-\frac{3}{4}$$

Subtract \frac{3}{4} from 2 to get \frac{5}{4}.

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

Factor

$$\frac{18x^{2}-2x+15}{12}$$

Solution Steps

Factor out \frac{1}{12}. Polynomial 18x^{2}-2x+15 is not factored since it does not have any rational roots.

$$\frac{18x^{2}-2x+15}{12}$$