Solve 5x^2+x^2-16x-12div(5x+6)

$$5 x ^ { 2 } + x ^ { 2 } - 16 x - 12 \div ( 5 x + 6 )$$

Evaluate

$$\frac{2\left(15x^{3}-22x^{2}-48x-6\right)}{5x+6}$$

Short Solution Steps

Combine 5x^{2} and x^{2} to get 6x^{2}.

$$6x^{2}-16x-\frac{12}{5x+6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 6x^{2}-16x times \frac{5x+6}{5x+6}.

$$\frac{\left(6x^{2}-16x\right)\left(5x+6\right)}{5x+6}-\frac{12}{5x+6}$$

Since \frac{\left(6x^{2}-16x\right)\left(5x+6\right)}{5x+6} and \frac{12}{5x+6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(6x^{2}-16x\right)\left(5x+6\right)-12}{5x+6}$$

Do the multiplications in \left(6x^{2}-16x\right)\left(5x+6\right)-12.

$$\frac{30x^{3}+36x^{2}-80x^{2}-96x-12}{5x+6}$$

Combine like terms in 30x^{3}+36x^{2}-80x^{2}-96x-12.

$$\frac{30x^{3}-44x^{2}-96x-12}{5x+6}$$

Differentiate w.r.t. x

$$\frac{4\left(75x^{3}+80x^{2}-132x-129\right)}{\left(5x+6\right)^{2}}$$