Solve (x+y)+(x-y)/2(x+y)(x-y)

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

Evaluate

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

Short Solution Steps

Combine x and x to get 2x.

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

Combine y and -y to get 0.

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

Cancel out 2 in both numerator and denominator.

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

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}.

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

Expand

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

Short Solution Steps

Combine x and x to get 2x.

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

Combine y and -y to get 0.

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

Cancel out 2 in both numerator and denominator.

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

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}.

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