Solve x^3+4x-21x/x^3-9xdiv2x+14/4x+12

$$\frac{ { x }^{ 3 } +4x-21x }{ { x }^{ 3 } -9x } \div \frac{ 2x+14 }{ 4x+12 }$$

Evaluate

$$\frac{2\left(x^{2}-17\right)}{\left(x-3\right)\left(x+7\right)}$$

Short Solution Steps

Divide \frac{x^{3}+4x-21x}{x^{3}-9x} by \frac{2x+14}{4x+12} by multiplying \frac{x^{3}+4x-21x}{x^{3}-9x} by the reciprocal of \frac{2x+14}{4x+12}.

$$\frac{\left(x^{3}+4x-21x\right)\left(4x+12\right)}{\left(x^{3}-9x\right)\left(2x+14\right)}$$

Combine 4x and -21x to get -17x.

$$\frac{\left(x^{3}-17x\right)\left(4x+12\right)}{\left(x^{3}-9x\right)\left(2x+14\right)}$$

Factor the expressions that are not already factored.

$$\frac{4x\left(x+3\right)\left(x^{2}-17\right)}{2x\left(x-3\right)\left(x+3\right)\left(x+7\right)}$$

Cancel out 2x\left(x+3\right) in both numerator and denominator.

$$\frac{2\left(x^{2}-17\right)}{\left(x-3\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{2x^{2}-34}{x^{2}+4x-21}$$

Expand

$$\frac{2\left(x^{2}-17\right)}{\left(x-3\right)\left(x+7\right)}$$

Short Solution Steps

Divide \frac{x^{3}+4x-21x}{x^{3}-9x} by \frac{2x+14}{4x+12} by multiplying \frac{x^{3}+4x-21x}{x^{3}-9x} by the reciprocal of \frac{2x+14}{4x+12}.

$$\frac{\left(x^{3}+4x-21x\right)\left(4x+12\right)}{\left(x^{3}-9x\right)\left(2x+14\right)}$$

Combine 4x and -21x to get -17x.

$$\frac{\left(x^{3}-17x\right)\left(4x+12\right)}{\left(x^{3}-9x\right)\left(2x+14\right)}$$

Factor the expressions that are not already factored.

$$\frac{4x\left(x+3\right)\left(x^{2}-17\right)}{2x\left(x-3\right)\left(x+3\right)\left(x+7\right)}$$

Cancel out 2x\left(x+3\right) in both numerator and denominator.

$$\frac{2\left(x^{2}-17\right)}{\left(x-3\right)\left(x+7\right)}$$

Expand the expression.

$$\frac{2x^{2}-34}{x^{2}+4x-21}$$