Solve y^2+3y+2/y^2+5y+6*y^2+7y+12/y^2+5y+4

$$\frac { y ^ { 2 } + 3 y + 2 } { y ^ { 2 } + 5 y + 6 } \times \frac { y ^ { 2 } + 7 y + 12 } { y ^ { 2 } + 5 y + 4 }$$

Evaluate

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Short Solution Steps

Factor the expressions that are not already factored in \frac{y^{2}+3y+2}{y^{2}+5y+6}.

$$\frac{\left(y+1\right)\left(y+2\right)}{\left(y+2\right)\left(y+3\right)}\times \frac{y^{2}+7y+12}{y^{2}+5y+4}$$

Cancel out y+2 in both numerator and denominator.

$$\frac{y+1}{y+3}\times \frac{y^{2}+7y+12}{y^{2}+5y+4}$$

Factor the expressions that are not already factored in \frac{y^{2}+7y+12}{y^{2}+5y+4}.

$$\frac{y+1}{y+3}\times \frac{\left(y+3\right)\left(y+4\right)}{\left(y+1\right)\left(y+4\right)}$$

Cancel out y+4 in both numerator and denominator.

$$\frac{y+1}{y+3}\times \frac{y+3}{y+1}$$

Multiply \frac{y+1}{y+3} times \frac{y+3}{y+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(y+1\right)\left(y+3\right)}{\left(y+3\right)\left(y+1\right)}$$

Cancel out \left(y+1\right)\left(y+3\right) in both numerator and denominator.

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Factor

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