Solve x^2-7x+12/x^2-2x-3*x^2+4x+16/x^3-64

$$\frac { x ^ { 2 } - 7 x + 12 } { x ^ { 2 } - 2 x - 3 } \times \frac { x ^ { 2 } + 4 x + 16 } { x ^ { 3 } - 64 }$$

Evaluate

$$\frac{1}{x+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-7x+12}{x^{2}-2x-3}.

$$\frac{\left(x-4\right)\left(x-3\right)}{\left(x-3\right)\left(x+1\right)}\times \frac{x^{2}+4x+16}{x^{3}-64}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x-4}{x+1}\times \frac{x^{2}+4x+16}{x^{3}-64}$$

Factor the expressions that are not already factored in \frac{x^{2}+4x+16}{x^{3}-64}.

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

Cancel out x^{2}+4x+16 in both numerator and denominator.

$$\frac{x-4}{x+1}\times \frac{1}{x-4}$$

Multiply \frac{x-4}{x+1} times \frac{1}{x-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x-4}{\left(x+1\right)\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{1}{x+1}$$

Expand

$$\frac{1}{x+1}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}-7x+12}{x^{2}-2x-3}.

$$\frac{\left(x-4\right)\left(x-3\right)}{\left(x-3\right)\left(x+1\right)}\times \frac{x^{2}+4x+16}{x^{3}-64}$$

Cancel out x-3 in both numerator and denominator.

$$\frac{x-4}{x+1}\times \frac{x^{2}+4x+16}{x^{3}-64}$$

Factor the expressions that are not already factored in \frac{x^{2}+4x+16}{x^{3}-64}.

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

Cancel out x^{2}+4x+16 in both numerator and denominator.

$$\frac{x-4}{x+1}\times \frac{1}{x-4}$$

Multiply \frac{x-4}{x+1} times \frac{1}{x-4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{x-4}{\left(x+1\right)\left(x-4\right)}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{1}{x+1}$$