Solve 3(x^2+9/x^2-9-/x

$$3 ( \frac { x ^ { 2 } + 9 } { x ^ { 2 } - 9 } - \frac { } { x }$$

Evaluate

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

Short Solution Steps

Factor x^{2}-9.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and x is x\left(x-3\right)\left(x+3\right). Multiply \frac{x^{2}+9}{\left(x-3\right)\left(x+3\right)} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}.

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

Since \frac{\left(x^{2}+9\right)x}{x\left(x-3\right)\left(x+3\right)} and \frac{\left(x-3\right)\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x^{2}+9\right)x-\left(x-3\right)\left(x+3\right).

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

Combine like terms in x^{3}+9x-x^{2}-3x+3x+9.

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

Express 3\times \frac{x^{3}+9x-x^{2}+9}{x\left(x-3\right)\left(x+3\right)} as a single fraction.

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

Use the distributive property to multiply 3 by x^{3}+9x-x^{2}+9.

$$\frac{3x^{3}+27x-3x^{2}+27}{x\left(x-3\right)\left(x+3\right)}$$

Use the distributive property to multiply x by x-3.

$$\frac{3x^{3}+27x-3x^{2}+27}{\left(x^{2}-3x\right)\left(x+3\right)}$$

Use the distributive property to multiply x^{2}-3x by x+3 and combine like terms.

$$\frac{3x^{3}+27x-3x^{2}+27}{x^{3}-9x}$$

Expand

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

Short Solution Steps

Factor x^{2}-9.

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

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(x-3\right)\left(x+3\right) and x is x\left(x-3\right)\left(x+3\right). Multiply \frac{x^{2}+9}{\left(x-3\right)\left(x+3\right)} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}.

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

Since \frac{\left(x^{2}+9\right)x}{x\left(x-3\right)\left(x+3\right)} and \frac{\left(x-3\right)\left(x+3\right)}{x\left(x-3\right)\left(x+3\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in \left(x^{2}+9\right)x-\left(x-3\right)\left(x+3\right).

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

Combine like terms in x^{3}+9x-x^{2}-3x+3x+9.

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

Express 3\times \frac{x^{3}+9x-x^{2}+9}{x\left(x-3\right)\left(x+3\right)} as a single fraction.

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

Use the distributive property to multiply 3 by x^{3}+9x-x^{2}+9.

$$\frac{3x^{3}+27x-3x^{2}+27}{x\left(x-3\right)\left(x+3\right)}$$

Use the distributive property to multiply x by x-3.

$$\frac{3x^{3}+27x-3x^{2}+27}{\left(x^{2}-3x\right)\left(x+3\right)}$$

Use the distributive property to multiply x^{2}-3x by x+3 and combine like terms.

$$\frac{3x^{3}+27x-3x^{2}+27}{x^{3}-9x}$$