Solve frac{2x^{2}-9x-18}{4x^2-24x}div2x^3+3x^2/x^2-16*1/x+4

$$\frac { 2 x ^ { 2 } - 9 x - 18 } { 4 x ^ { 2 } - 24 x } \div \frac { 2 x ^ { 3 } + 3 x ^ { 2 } } { x ^ { 2 } - 16 } \times \frac { 1 } { x + 4 }$$

Evaluate

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

Short Solution Steps

Divide \frac{2x^{2}-9x-18}{4x^{2}-24x} by \frac{2x^{3}+3x^{2}}{x^{2}-16} by multiplying \frac{2x^{2}-9x-18}{4x^{2}-24x} by the reciprocal of \frac{2x^{3}+3x^{2}}{x^{2}-16}.

$$\frac{\left(2x^{2}-9x-18\right)\left(x^{2}-16\right)}{\left(4x^{2}-24x\right)\left(2x^{3}+3x^{2}\right)}\times \frac{1}{x+4}$$

Factor the expressions that are not already factored in \frac{\left(2x^{2}-9x-18\right)\left(x^{2}-16\right)}{\left(4x^{2}-24x\right)\left(2x^{3}+3x^{2}\right)}.

$$\frac{\left(x-6\right)\left(x-4\right)\left(x+4\right)\left(2x+3\right)}{4x\left(x-6\right)\left(2x+3\right)x^{2}}\times \frac{1}{x+4}$$

Cancel out \left(x-6\right)\left(2x+3\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+4\right)}{4xx^{2}}\times \frac{1}{x+4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x-4\right)\left(x+4\right)}{4x^{3}}\times \frac{1}{x+4}$$

Multiply \frac{\left(x-4\right)\left(x+4\right)}{4x^{3}} times \frac{1}{x+4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+4 in both numerator and denominator.

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

Expand

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

Short Solution Steps

Divide \frac{2x^{2}-9x-18}{4x^{2}-24x} by \frac{2x^{3}+3x^{2}}{x^{2}-16} by multiplying \frac{2x^{2}-9x-18}{4x^{2}-24x} by the reciprocal of \frac{2x^{3}+3x^{2}}{x^{2}-16}.

$$\frac{\left(2x^{2}-9x-18\right)\left(x^{2}-16\right)}{\left(4x^{2}-24x\right)\left(2x^{3}+3x^{2}\right)}\times \frac{1}{x+4}$$

Factor the expressions that are not already factored in \frac{\left(2x^{2}-9x-18\right)\left(x^{2}-16\right)}{\left(4x^{2}-24x\right)\left(2x^{3}+3x^{2}\right)}.

$$\frac{\left(x-6\right)\left(x-4\right)\left(x+4\right)\left(2x+3\right)}{4x\left(x-6\right)\left(2x+3\right)x^{2}}\times \frac{1}{x+4}$$

Cancel out \left(x-6\right)\left(2x+3\right) in both numerator and denominator.

$$\frac{\left(x-4\right)\left(x+4\right)}{4xx^{2}}\times \frac{1}{x+4}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\left(x-4\right)\left(x+4\right)}{4x^{3}}\times \frac{1}{x+4}$$

Multiply \frac{\left(x-4\right)\left(x+4\right)}{4x^{3}} times \frac{1}{x+4} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out x+4 in both numerator and denominator.

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