Solve =(100+x)^2+x^2-((x+100)^2-x^2)/2(100+x)(x)

$$= \frac { ( 100 + x ) ^ { 2 } + x ^ { 2 } - ( ( x + 100 ) ^ { 2 } - x ^ { 2 } ) } { 2 ( 100 + x ) ( x ) }$$

Evaluate

$$\frac{x}{x+100}$$

Solution Steps

To find the opposite of \left(x+100\right)^{2}-x^{2}, find the opposite of each term.

$$\frac{\left(100+x\right)^{2}+x^{2}-\left(x+100\right)^{2}+x^{2}}{2\left(100+x\right)x}$$

Combine \left(100+x\right)^{2} and -\left(x+100\right)^{2} to get 0.

$$\frac{x^{2}+x^{2}}{2\left(100+x\right)x}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$\frac{2x^{2}}{2\left(100+x\right)x}$$

Cancel out 2x in both numerator and denominator.

$$\frac{x}{x+100}$$

Expand

$$\frac{x}{x+100}$$

Solution Steps

To find the opposite of \left(x+100\right)^{2}-x^{2}, find the opposite of each term.

$$\frac{\left(100+x\right)^{2}+x^{2}-\left(x+100\right)^{2}+x^{2}}{2\left(100+x\right)x}$$

Combine \left(100+x\right)^{2} and -\left(x+100\right)^{2} to get 0.

$$\frac{x^{2}+x^{2}}{2\left(100+x\right)x}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$\frac{2x^{2}}{2\left(100+x\right)x}$$

Cancel out 2x in both numerator and denominator.

$$\frac{x}{x+100}$$