# Simplification changes the output?

if I have a function $f(x)=\frac{2x}{x+1}$ I can simplify it to $f(x) =\frac{2}{1}=2$

But this changes the function for example $f(10)=\frac{20}{11}$ which is not equal to 2. Does this mean if I simplify a function it will become a different function?

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We have $\frac{2x}{x+1} \neq 2$ for all $x \neq -1$. What do you mean by "simplify"? –  dtldarek Feb 10 at 15:58
You cannot simplify it in that way. –  ciceksiz kakarot Feb 10 at 16:09
Why can't I get rid of the x? –  Maik Klein Feb 10 at 16:56
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## 1 Answer

Note that

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

Remember that

$$\frac{a}{b} - c = \frac{a}{b} - \frac{c}{1} = \frac{a - b c}{b}$$

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