Solve x^2+1/x-6*x^2-36/x^3+x

$$\frac { x ^ { 2 } + 1 } { x - 6 } \cdot \frac { x ^ { 2 } - 36 } { x ^ { 3 } + x }$$

Evaluate

$$\frac{x+6}{x}$$

Short Solution Steps

Multiply \frac{x^{2}+1}{x-6} times \frac{x^{2}-36}{x^{3}+x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+1\right)\left(x^{2}-36\right)}{\left(x-6\right)\left(x^{3}+x\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-6\right)\left(x^{2}+1\right) in both numerator and denominator.

$$\frac{x+6}{x}$$

Expand

$$\frac{x+6}{x}$$

Short Solution Steps

Multiply \frac{x^{2}+1}{x-6} times \frac{x^{2}-36}{x^{3}+x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x^{2}+1\right)\left(x^{2}-36\right)}{\left(x-6\right)\left(x^{3}+x\right)}$$

Factor the expressions that are not already factored.

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

Cancel out \left(x-6\right)\left(x^{2}+1\right) in both numerator and denominator.

$$\frac{x+6}{x}$$