Solve x+2/(x^2+1)(x-1)div(x+2)(x-2)/x^5

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

Evaluate

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

Short Solution Steps

Divide \frac{x+2}{\left(x^{2}+1\right)\left(x-1\right)} by \frac{\left(x+2\right)\left(x-2\right)}{x^{5}} by multiplying \frac{x+2}{\left(x^{2}+1\right)\left(x-1\right)} by the reciprocal of \frac{\left(x+2\right)\left(x-2\right)}{x^{5}}.

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

Cancel out x+2 in both numerator and denominator.

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

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

$$\frac{x^{5}}{\left(x^{2}-3x+2\right)\left(x^{2}+1\right)}$$

Use the distributive property to multiply x^{2}-3x+2 by x^{2}+1 and combine like terms.

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

Expand

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

Short Solution Steps

Divide \frac{x+2}{\left(x^{2}+1\right)\left(x-1\right)} by \frac{\left(x+2\right)\left(x-2\right)}{x^{5}} by multiplying \frac{x+2}{\left(x^{2}+1\right)\left(x-1\right)} by the reciprocal of \frac{\left(x+2\right)\left(x-2\right)}{x^{5}}.

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

Cancel out x+2 in both numerator and denominator.

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

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

$$\frac{x^{5}}{\left(x^{2}-3x+2\right)\left(x^{2}+1\right)}$$

Use the distributive property to multiply x^{2}-3x+2 by x^{2}+1 and combine like terms.

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