Solve frac{5x^{3}-15x^2}{x+3}-10x^3+15x^2/5x^2+2x

$$\frac { 5 x ^ { 3 } - 15 x ^ { 2 } } { x + 3 } - \frac { 10 x ^ { 3 } + 15 x ^ { 2 } } { 5 x ^ { 2 } } + 2 x$$

Evaluate

$$\frac{5x^{3}-15x^{2}-3x-9}{x+3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{10x^{3}+15x^{2}}{5x^{2}}.

$$\frac{5x^{3}-15x^{2}}{x+3}-\frac{5\left(2x+3\right)x^{2}}{5x^{2}}+2x$$

Cancel out 5x^{2} in both numerator and denominator.

$$\frac{5x^{3}-15x^{2}}{x+3}-\left(2x+3\right)+2x$$

To find the opposite of 2x+3, find the opposite of each term.

$$\frac{5x^{3}-15x^{2}}{x+3}-2x-3+2x$$

Combine -2x and 2x to get 0.

$$\frac{5x^{3}-15x^{2}}{x+3}-3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+3}{x+3}.

$$\frac{5x^{3}-15x^{2}}{x+3}-\frac{3\left(x+3\right)}{x+3}$$

Since \frac{5x^{3}-15x^{2}}{x+3} and \frac{3\left(x+3\right)}{x+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x^{3}-15x^{2}-3\left(x+3\right)}{x+3}$$

Do the multiplications in 5x^{3}-15x^{2}-3\left(x+3\right).

$$\frac{5x^{3}-15x^{2}-3x-9}{x+3}$$

Expand

$$\frac{5x^{3}-15x^{2}-3x-9}{x+3}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{10x^{3}+15x^{2}}{5x^{2}}.

$$\frac{5x^{3}-15x^{2}}{x+3}-\frac{5\left(2x+3\right)x^{2}}{5x^{2}}+2x$$

Cancel out 5x^{2} in both numerator and denominator.

$$\frac{5x^{3}-15x^{2}}{x+3}-\left(2x+3\right)+2x$$

To find the opposite of 2x+3, find the opposite of each term.

$$\frac{5x^{3}-15x^{2}}{x+3}-2x-3+2x$$

Combine -2x and 2x to get 0.

$$\frac{5x^{3}-15x^{2}}{x+3}-3$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x+3}{x+3}.

$$\frac{5x^{3}-15x^{2}}{x+3}-\frac{3\left(x+3\right)}{x+3}$$

Since \frac{5x^{3}-15x^{2}}{x+3} and \frac{3\left(x+3\right)}{x+3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5x^{3}-15x^{2}-3\left(x+3\right)}{x+3}$$

Do the multiplications in 5x^{3}-15x^{2}-3\left(x+3\right).

$$\frac{5x^{3}-15x^{2}-3x-9}{x+3}$$