Solve 8y^2-x^24^2/4^2{x^2-4{y}^2}

$$\frac{ 8 { y }^{ 2 } - { x }^{ 2 } { 4 }^{ 2 } }{ { 4 }^{ 2 } { x }^{ 2 } -4 { y }^{ 2 } }$$

Evaluate

$$\frac{2\left(y^{2}-2x^{2}\right)}{4x^{2}-y^{2}}$$

Short Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{8y^{2}-x^{2}\times 16}{4^{2}x^{2}-4y^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8y^{2}-x^{2}\times 16}{16x^{2}-4y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{8\left(-2x^{2}+y^{2}\right)}{4\left(2x+y\right)\left(2x-y\right)}$$

Cancel out 4 in both numerator and denominator.

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

Expand the expression.

$$\frac{-4x^{2}+2y^{2}}{4x^{2}-y^{2}}$$

Expand

$$-\frac{2\left(2x^{2}-y^{2}\right)}{4x^{2}-y^{2}}$$

Short Solution Steps

Calculate 4 to the power of 2 and get 16.

$$\frac{8y^{2}-x^{2}\times 16}{4^{2}x^{2}-4y^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8y^{2}-x^{2}\times 16}{16x^{2}-4y^{2}}$$

Factor the expressions that are not already factored.

$$\frac{8\left(-2x^{2}+y^{2}\right)}{4\left(2x+y\right)\left(2x-y\right)}$$

Cancel out 4 in both numerator and denominator.

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

Expand the expression.

$$\frac{-4x^{2}+2y^{2}}{4x^{2}-y^{2}}$$