Solve x^2+3x/2+x-3x^2/8

$$\frac{ { x }^{ 2 } +3x }{ 2 } + \frac{ x-3 { x }^{ 2 } }{ 8 }$$

Evaluate

$$\frac{x\left(x+13\right)}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 8 is 8. Multiply \frac{x^{2}+3x}{2} times \frac{4}{4}.

$$\frac{4\left(x^{2}+3x\right)}{8}+\frac{x-3x^{2}}{8}$$

Since \frac{4\left(x^{2}+3x\right)}{8} and \frac{x-3x^{2}}{8} have the same denominator, add them by adding their numerators.

$$\frac{4\left(x^{2}+3x\right)+x-3x^{2}}{8}$$

Do the multiplications in 4\left(x^{2}+3x\right)+x-3x^{2}.

$$\frac{4x^{2}+12x+x-3x^{2}}{8}$$

Combine like terms in 4x^{2}+12x+x-3x^{2}.

$$\frac{x^{2}+13x}{8}$$

Expand

$$\frac{x^{2}+13x}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 8 is 8. Multiply \frac{x^{2}+3x}{2} times \frac{4}{4}.

$$\frac{4\left(x^{2}+3x\right)}{8}+\frac{x-3x^{2}}{8}$$

Since \frac{4\left(x^{2}+3x\right)}{8} and \frac{x-3x^{2}}{8} have the same denominator, add them by adding their numerators.

$$\frac{4\left(x^{2}+3x\right)+x-3x^{2}}{8}$$

Do the multiplications in 4\left(x^{2}+3x\right)+x-3x^{2}.

$$\frac{4x^{2}+12x+x-3x^{2}}{8}$$

Combine like terms in 4x^{2}+12x+x-3x^{2}.

$$\frac{x^{2}+13x}{8}$$