Evaluate
\frac{\left(40-x\right)\left(x+60\right)}{2x\left(x+20\right)}
Expand
-\frac{x^{2}+20x-2400}{2x\left(x+20\right)}
Graph
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\frac{80}{x}-\frac{180x+800+x^{2}}{2x\left(x+20\right)}
Factor 2x^{2}+40x.
\frac{80\times 2\left(x+20\right)}{2x\left(x+20\right)}-\frac{180x+800+x^{2}}{2x\left(x+20\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 2x\left(x+20\right) is 2x\left(x+20\right). Multiply \frac{80}{x} times \frac{2\left(x+20\right)}{2\left(x+20\right)}.
\frac{80\times 2\left(x+20\right)-\left(180x+800+x^{2}\right)}{2x\left(x+20\right)}
Since \frac{80\times 2\left(x+20\right)}{2x\left(x+20\right)} and \frac{180x+800+x^{2}}{2x\left(x+20\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{160x+3200-180x-800-x^{2}}{2x\left(x+20\right)}
Do the multiplications in 80\times 2\left(x+20\right)-\left(180x+800+x^{2}\right).
\frac{-20x+2400-x^{2}}{2x\left(x+20\right)}
Combine like terms in 160x+3200-180x-800-x^{2}.
\frac{-20x+2400-x^{2}}{2x^{2}+40x}
Expand 2x\left(x+20\right).
\frac{80}{x}-\frac{180x+800+x^{2}}{2x\left(x+20\right)}
Factor 2x^{2}+40x.
\frac{80\times 2\left(x+20\right)}{2x\left(x+20\right)}-\frac{180x+800+x^{2}}{2x\left(x+20\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x and 2x\left(x+20\right) is 2x\left(x+20\right). Multiply \frac{80}{x} times \frac{2\left(x+20\right)}{2\left(x+20\right)}.
\frac{80\times 2\left(x+20\right)-\left(180x+800+x^{2}\right)}{2x\left(x+20\right)}
Since \frac{80\times 2\left(x+20\right)}{2x\left(x+20\right)} and \frac{180x+800+x^{2}}{2x\left(x+20\right)} have the same denominator, subtract them by subtracting their numerators.
\frac{160x+3200-180x-800-x^{2}}{2x\left(x+20\right)}
Do the multiplications in 80\times 2\left(x+20\right)-\left(180x+800+x^{2}\right).
\frac{-20x+2400-x^{2}}{2x\left(x+20\right)}
Combine like terms in 160x+3200-180x-800-x^{2}.
\frac{-20x+2400-x^{2}}{2x^{2}+40x}
Expand 2x\left(x+20\right).
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Limits
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