Solve 2x^4+17x^3-10x^3-3-14xdiv(-3+x)=

$$2 { x }^{ 4 } +17 { x }^{ 3 } -10 { x }^{ 3 } -3-14x \div (-3+x)=$$

Evaluate

$$\frac{2x^{5}+x^{4}-21x^{3}-17x+9}{x-3}$$

Short Solution Steps

Combine 17x^{3} and -10x^{3} to get 7x^{3}.

$$2x^{4}+7x^{3}-3-\frac{14x}{-3+x}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2x^{4}+7x^{3}-3 times \frac{-3+x}{-3+x}.

$$\frac{\left(2x^{4}+7x^{3}-3\right)\left(-3+x\right)}{-3+x}-\frac{14x}{-3+x}$$

Since \frac{\left(2x^{4}+7x^{3}-3\right)\left(-3+x\right)}{-3+x} and \frac{14x}{-3+x} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(2x^{4}+7x^{3}-3\right)\left(-3+x\right)-14x}{-3+x}$$

Do the multiplications in \left(2x^{4}+7x^{3}-3\right)\left(-3+x\right)-14x.

$$\frac{-6x^{4}+2x^{5}-21x^{3}+7x^{4}+9-3x-14x}{-3+x}$$

Combine like terms in -6x^{4}+2x^{5}-21x^{3}+7x^{4}+9-3x-14x.

$$\frac{x^{4}+2x^{5}-21x^{3}+9-17x}{-3+x}$$

Differentiate w.r.t. x

$$\frac{8x^{5}-27x^{4}-54x^{3}+189x^{2}+42}{\left(x-3\right)^{2}}$$