Solve (x+y)^2/x^2-v^2:x+y/x-y=

$$\frac { ( x + y ) ^ { 2 } } { x ^ { 2 } - v ^ { 2 } } : \frac { x + y } { x - y } =$$

Evaluate

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

Short Solution Steps

Divide \frac{\left(x+y\right)^{2}}{x^{2}-v^{2}} by \frac{x+y}{x-y} by multiplying \frac{\left(x+y\right)^{2}}{x^{2}-v^{2}} by the reciprocal of \frac{x+y}{x-y}.

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

Cancel out x+y in both numerator and denominator.

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

Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

Expand

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

Short Solution Steps

Divide \frac{\left(x+y\right)^{2}}{x^{2}-v^{2}} by \frac{x+y}{x-y} by multiplying \frac{\left(x+y\right)^{2}}{x^{2}-v^{2}} by the reciprocal of \frac{x+y}{x-y}.

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

Cancel out x+y in both numerator and denominator.

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

Consider \left(x+y\right)\left(x-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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