Solve 2x^2+8xy+8y^2/x^2+4xy+4y^2frac{2{x}^2+7xy+6{y}^2}{4{x}^2+14xy+12{y}^2}

$$\frac{ 2 { x }^{ 2 } +8xy+8 { y }^{ 2 } }{ { x }^{ 2 } +4xy+4 { y }^{ 2 } } \frac{ 2 { x }^{ 2 } +7xy+6 { y }^{ 2 } }{ 4 { x }^{ 2 } +14xy+12 { y }^{ 2 } }$$

Evaluate

$$1$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{2x^{2}+8xy+8y^{2}}{x^{2}+4xy+4y^{2}}.

$$\frac{2\left(x+2y\right)^{2}}{\left(x+2y\right)^{2}}\times \frac{2x^{2}+7xy+6y^{2}}{4x^{2}+14xy+12y^{2}}$$

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

$$2\times \frac{2x^{2}+7xy+6y^{2}}{4x^{2}+14xy+12y^{2}}$$

Factor the expressions that are not already factored in \frac{2x^{2}+7xy+6y^{2}}{4x^{2}+14xy+12y^{2}}.

$$2\times \frac{\left(x+2y\right)\left(2x+3y\right)}{2\left(x+2y\right)\left(2x+3y\right)}$$

Cancel out \left(x+2y\right)\left(2x+3y\right) in both numerator and denominator.

$$2\times \frac{1}{2}$$

Multiply 2 and \frac{1}{2} to get 1.

$$1$$

Factor

$$1$$