Solve m^2/3+5x-3x^2+9/6-2/3

$$\frac { m ^ { 2 } } { 3 } + 5 x - 3 x ^ { 2 } + \frac { 9 } { 6 } - \frac { 2 } { 3 }$$

Evaluate

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

Short Solution Steps

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

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

Subtract \frac{2}{3} from \frac{3}{2} to get \frac{5}{6}.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 3 and 6 is 6. Multiply \frac{m^{2}}{3} times \frac{2}{2}.

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

Since \frac{2m^{2}}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 5x-3x^{2} times \frac{6}{6}.

$$\frac{2m^{2}+5}{6}+\frac{6\left(5x-3x^{2}\right)}{6}$$

Since \frac{2m^{2}+5}{6} and \frac{6\left(5x-3x^{2}\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{2m^{2}+5+6\left(5x-3x^{2}\right)}{6}$$

Do the multiplications in 2m^{2}+5+6\left(5x-3x^{2}\right).

$$\frac{2m^{2}+5+30x-18x^{2}}{6}$$

Factor

$$\frac{5+2m^{2}+30x-18x^{2}}{6}$$

Solution Steps

Factor out \frac{1}{6}.

$$\frac{2m^{2}+30x-18x^{2}+5}{6}$$