Solve (16/x+2-5+x)divx-1/x^2-9

$$( \frac { 16 } { x + 2 } - 5 + x ) \div \frac { x - 1 } { x ^ { 2 } - 9 }$$

Evaluate

$$\frac{\left(x^{2}-9\right)\left(x^{2}-3x+6\right)}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -5+x times \frac{x+2}{x+2}.

$$\frac{\frac{16}{x+2}+\frac{\left(-5+x\right)\left(x+2\right)}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Since \frac{16}{x+2} and \frac{\left(-5+x\right)\left(x+2\right)}{x+2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{16+\left(-5+x\right)\left(x+2\right)}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Do the multiplications in 16+\left(-5+x\right)\left(x+2\right).

$$\frac{\frac{16-5x-10+x^{2}+2x}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Combine like terms in 16-5x-10+x^{2}+2x.

$$\frac{\frac{6-3x+x^{2}}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Divide \frac{6-3x+x^{2}}{x+2} by \frac{x-1}{x^{2}-9} by multiplying \frac{6-3x+x^{2}}{x+2} by the reciprocal of \frac{x-1}{x^{2}-9}.

$$\frac{\left(6-3x+x^{2}\right)\left(x^{2}-9\right)}{\left(x+2\right)\left(x-1\right)}$$

Use the distributive property to multiply 6-3x+x^{2} by x^{2}-9 and combine like terms.

$$\frac{-3x^{2}-54-3x^{3}+27x+x^{4}}{\left(x+2\right)\left(x-1\right)}$$

Use the distributive property to multiply x+2 by x-1 and combine like terms.

$$\frac{-3x^{2}-54-3x^{3}+27x+x^{4}}{x^{2}+x-2}$$

Expand

$$\frac{x^{4}-3x^{3}-3x^{2}+27x-54}{\left(x-1\right)\left(x+2\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply -5+x times \frac{x+2}{x+2}.

$$\frac{\frac{16}{x+2}+\frac{\left(-5+x\right)\left(x+2\right)}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Since \frac{16}{x+2} and \frac{\left(-5+x\right)\left(x+2\right)}{x+2} have the same denominator, add them by adding their numerators.

$$\frac{\frac{16+\left(-5+x\right)\left(x+2\right)}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Do the multiplications in 16+\left(-5+x\right)\left(x+2\right).

$$\frac{\frac{16-5x-10+x^{2}+2x}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Combine like terms in 16-5x-10+x^{2}+2x.

$$\frac{\frac{6-3x+x^{2}}{x+2}}{\frac{x-1}{x^{2}-9}}$$

Divide \frac{6-3x+x^{2}}{x+2} by \frac{x-1}{x^{2}-9} by multiplying \frac{6-3x+x^{2}}{x+2} by the reciprocal of \frac{x-1}{x^{2}-9}.

$$\frac{\left(6-3x+x^{2}\right)\left(x^{2}-9\right)}{\left(x+2\right)\left(x-1\right)}$$

Use the distributive property to multiply 6-3x+x^{2} by x^{2}-9 and combine like terms.

$$\frac{-3x^{2}-54-3x^{3}+27x+x^{4}}{\left(x+2\right)\left(x-1\right)}$$

Use the distributive property to multiply x+2 by x-1 and combine like terms.

$$\frac{-3x^{2}-54-3x^{3}+27x+x^{4}}{x^{2}+x-2}$$