Solve 3x^3-4x^2+2/3+4x

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

Evaluate

$$\frac{12x^{4}-7x^{3}-12x^{2}+2}{4x+3}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x^{3}-4x^{2} times \frac{3+4x}{3+4x}.

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

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

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

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

$$\frac{9x^{3}+12x^{4}-12x^{2}-16x^{3}+2}{3+4x}$$

Combine like terms in 9x^{3}+12x^{4}-12x^{2}-16x^{3}+2.

$$\frac{-7x^{3}+12x^{4}-12x^{2}+2}{3+4x}$$

Differentiate w.r.t. x

$$\frac{144x^{4}+88x^{3}-111x^{2}-72x-8}{\left(4x+3\right)^{2}}$$