Solve x(x+1)/2-y(y-1)/2

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

Evaluate

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

Short Solution Steps

Since \frac{x\left(x+1\right)}{2} and \frac{y\left(y-1\right)}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x\left(x+1\right)-y\left(y-1\right).

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

Expand

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

Short Solution Steps

Since \frac{x\left(x+1\right)}{2} and \frac{y\left(y-1\right)}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x\left(x+1\right)-y\left(y-1\right).

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