Solve 2x^2+9x+2x^2+16/(2x^2+9x+16x+72)x-2x^2+16x+7x+72/1=

$$\frac { 2 x ^ { 2 } + 9 x + 2 x ^ { 2 } + 16 } { ( 2 x ^ { 2 } + 9 x + 16 x + 72 ) x } - \frac { 2 x ^ { 2 } + 16 x + 7 x + 72 } { 1 } =$$

Evaluate

$$\frac{16-5175x-3452x^{2}-863x^{3}-96x^{4}-4x^{5}}{x\left(x+8\right)\left(2x+9\right)}$$

Short Solution Steps

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+9x+16x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Combine 9x and 16x to get 25x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Combine 16x and 7x to get 23x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+23x+72}{1}$$

Anything divided by one gives itself.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\left(2x^{2}+23x+72\right)$$

To find the opposite of 2x^{2}+23x+72, find the opposite of each term.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-2x^{2}-23x-72$$

Factor \left(2x^{2}+25x+72\right)x.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-23x-72$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x^{2}-23x-72 times \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Since \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} and \frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Do the multiplications in 4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right).

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

Combine like terms in 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

Expand x\left(x+8\right)\left(2x+9\right).

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{2x^{3}+25x^{2}+72x}$$

Expand

$$\frac{16-5175x-3452x^{2}-863x^{3}-96x^{4}-4x^{5}}{x\left(2x^{2}+25x+72\right)}$$

Short Solution Steps

Combine 2x^{2} and 2x^{2} to get 4x^{2}.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+9x+16x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Combine 9x and 16x to get 25x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+16x+7x+72}{1}$$

Combine 16x and 7x to get 23x.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\frac{2x^{2}+23x+72}{1}$$

Anything divided by one gives itself.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-\left(2x^{2}+23x+72\right)$$

To find the opposite of 2x^{2}+23x+72, find the opposite of each term.

$$\frac{4x^{2}+9x+16}{\left(2x^{2}+25x+72\right)x}-2x^{2}-23x-72$$

Factor \left(2x^{2}+25x+72\right)x.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}-2x^{2}-23x-72$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -2x^{2}-23x-72 times \frac{x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}.

$$\frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)}+\frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Since \frac{4x^{2}+9x+16}{x\left(x+8\right)\left(2x+9\right)} and \frac{\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)} have the same denominator, add them by adding their numerators.

$$\frac{4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right)}{x\left(x+8\right)\left(2x+9\right)}$$

Do the multiplications in 4x^{2}+9x+16+\left(-2x^{2}-23x-72\right)x\left(x+8\right)\left(2x+9\right).

$$\frac{4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x}{x\left(x+8\right)\left(2x+9\right)}$$

Combine like terms in 4x^{2}+9x+16-4x^{5}-50x^{4}-144x^{3}-46x^{4}-575x^{3}-1656x^{2}-144x^{3}-1800x^{2}-5184x.

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{x\left(x+8\right)\left(2x+9\right)}$$

Expand x\left(x+8\right)\left(2x+9\right).

$$\frac{-3452x^{2}-5175x+16-4x^{5}-96x^{4}-863x^{3}}{2x^{3}+25x^{2}+72x}$$