Solve x^2+5x+6/x^2+7x+12x^2-16/x^2+x-20x+5/x+2

$$\frac{ { x }^{ 2 } +5x+6 }{ { x }^{ 2 } +7x+12 } \frac{ { x }^{ 2 } -16 }{ { x }^{ 2 } +x-20 } \frac{ x+5 }{ x+2 }$$

Evaluate

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Short Solution Steps

Factor the expressions that are not already factored in \frac{x^{2}+5x+6}{x^{2}+7x+12}.

$$\frac{\left(x+2\right)\left(x+3\right)}{\left(x+3\right)\left(x+4\right)}\times \frac{x^{2}-16}{x^{2}+x-20}\times \frac{x+5}{x+2}$$

Cancel out x+3 in both numerator and denominator.

$$\frac{x+2}{x+4}\times \frac{x^{2}-16}{x^{2}+x-20}\times \frac{x+5}{x+2}$$

Factor the expressions that are not already factored in \frac{x^{2}-16}{x^{2}+x-20}.

$$\frac{x+2}{x+4}\times \frac{\left(x-4\right)\left(x+4\right)}{\left(x-4\right)\left(x+5\right)}\times \frac{x+5}{x+2}$$

Cancel out x-4 in both numerator and denominator.

$$\frac{x+2}{x+4}\times \frac{x+4}{x+5}\times \frac{x+5}{x+2}$$

Multiply \frac{x+2}{x+4} times \frac{x+4}{x+5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(x+2\right)\left(x+4\right)}{\left(x+4\right)\left(x+5\right)}\times \frac{x+5}{x+2}$$

Cancel out x+4 in both numerator and denominator.

$$\frac{x+2}{x+5}\times \frac{x+5}{x+2}$$

Multiply \frac{x+2}{x+5} times \frac{x+5}{x+2} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out \left(x+2\right)\left(x+5\right) in both numerator and denominator.

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Factor

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