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

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

Evaluate

$$\frac{\left(x-6\right)\left(x^{2}+16\right)}{4\left(x+1\right)x^{4}}$$

Short Solution Steps

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

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

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

$$\frac{\left(x-6\right)\left(2x+3\right)\left(x^{2}+16\right)}{4\left(2x+3\right)\left(x^{2}\right)^{2}}\times \frac{1}{x+1}$$

Cancel out 2x+3 in both numerator and denominator.

$$\frac{\left(x-6\right)\left(x^{2}+16\right)}{4\left(x^{2}\right)^{2}}\times \frac{1}{x+1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(x-6\right)\left(x^{2}+16\right)}{4x^{4}}\times \frac{1}{x+1}$$

Multiply \frac{\left(x-6\right)\left(x^{2}+16\right)}{4x^{4}} times \frac{1}{x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-6\right)\left(x^{2}+16\right)}{4x^{4}\left(x+1\right)}$$

Use the distributive property to multiply x-6 by x^{2}+16.

$$\frac{x^{3}+16x-6x^{2}-96}{4x^{4}\left(x+1\right)}$$

Use the distributive property to multiply 4x^{4} by x+1.

$$\frac{x^{3}+16x-6x^{2}-96}{4x^{5}+4x^{4}}$$

Expand

$$\frac{x^{3}-6x^{2}+16x-96}{4\left(x+1\right)x^{4}}$$

Short Solution Steps

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

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

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

$$\frac{\left(x-6\right)\left(2x+3\right)\left(x^{2}+16\right)}{4\left(2x+3\right)\left(x^{2}\right)^{2}}\times \frac{1}{x+1}$$

Cancel out 2x+3 in both numerator and denominator.

$$\frac{\left(x-6\right)\left(x^{2}+16\right)}{4\left(x^{2}\right)^{2}}\times \frac{1}{x+1}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\left(x-6\right)\left(x^{2}+16\right)}{4x^{4}}\times \frac{1}{x+1}$$

Multiply \frac{\left(x-6\right)\left(x^{2}+16\right)}{4x^{4}} times \frac{1}{x+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x-6\right)\left(x^{2}+16\right)}{4x^{4}\left(x+1\right)}$$

Use the distributive property to multiply x-6 by x^{2}+16.

$$\frac{x^{3}+16x-6x^{2}-96}{4x^{4}\left(x+1\right)}$$

Use the distributive property to multiply 4x^{4} by x+1.

$$\frac{x^{3}+16x-6x^{2}-96}{4x^{5}+4x^{4}}$$