Solve 2x^2+1/2+3x^2-5/3

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

Evaluate

$$2x^{2}-\frac{7}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{2x^{2}+1}{2} times \frac{3}{3}. Multiply \frac{3x^{2}-5}{3} times \frac{2}{2}.

$$\frac{3\left(2x^{2}+1\right)}{6}+\frac{2\left(3x^{2}-5\right)}{6}$$

Since \frac{3\left(2x^{2}+1\right)}{6} and \frac{2\left(3x^{2}-5\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\left(2x^{2}+1\right)+2\left(3x^{2}-5\right)}{6}$$

Do the multiplications in 3\left(2x^{2}+1\right)+2\left(3x^{2}-5\right).

$$\frac{6x^{2}+3+6x^{2}-10}{6}$$

Combine like terms in 6x^{2}+3+6x^{2}-10.

$$\frac{12x^{2}-7}{6}$$

Expand

$$2x^{2}-\frac{7}{6}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{2x^{2}+1}{2} times \frac{3}{3}. Multiply \frac{3x^{2}-5}{3} times \frac{2}{2}.

$$\frac{3\left(2x^{2}+1\right)}{6}+\frac{2\left(3x^{2}-5\right)}{6}$$

Since \frac{3\left(2x^{2}+1\right)}{6} and \frac{2\left(3x^{2}-5\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\left(2x^{2}+1\right)+2\left(3x^{2}-5\right)}{6}$$

Do the multiplications in 3\left(2x^{2}+1\right)+2\left(3x^{2}-5\right).

$$\frac{6x^{2}+3+6x^{2}-10}{6}$$

Combine like terms in 6x^{2}+3+6x^{2}-10.

$$\frac{12x^{2}-7}{6}$$