Solve x^2/4y^2-x^2+1):(1-x/x-2y)

$$\frac { x ^ { 2 } } { 4 y ^ { 2 } - x ^ { 2 } } + 1 ) : ( 1 - \frac { x } { x - 2 y } )$$

Evaluate

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

Short Solution Steps

Factor 4y^{2}-x^{2}.

$$\frac{x^{2}}{\left(x+2y\right)\left(-x+2y\right)}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{\left(x+2y\right)\left(-x+2y\right)}{\left(x+2y\right)\left(-x+2y\right)}.

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

Since \frac{x^{2}}{\left(x+2y\right)\left(-x+2y\right)} and \frac{\left(x+2y\right)\left(-x+2y\right)}{\left(x+2y\right)\left(-x+2y\right)} have the same denominator, add them by adding their numerators.

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

Do the multiplications in x^{2}+\left(x+2y\right)\left(-x+2y\right).

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

Combine like terms in x^{2}-x^{2}+2xy-2yx+4y^{2}.

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

Expand \left(x+2y\right)\left(-x+2y\right).

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

Differentiate w.r.t. x

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