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Basic Fraction Rule Question Watch

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    Hi there,

    So I know that if you have (a+b)/2, that is the same as a/2 +b/2

    However, if you have 1/(a+b), how come that isn't the same as 1/a + 1/b?

    Why is that? How come you can split the numerator up but not the denominator (if that makes sense)?
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    (Original post by vector12)
    Hi there,

    So I know that if you have (a+b)/2, that is the same as a/2 +b/2

    However, if you have 1/(a+b), how come that isn't the same as 1/a + 1/b?

    Why is that? How come you can split the numerator up but not the denominator (if that makes sense)?
    Because we don't define addition of fractions in that way.

    We are allowed to split the numerator because all the numerator is is just \frac{x}{y}=x(\frac{1}{y}) - so x lots of 1/y

    Meaning I can split x in such a way that a+b=x hence I have (a+b)(\frac{1}{y})=a(\frac{1}{y}  )+b(\frac{1}{y})=\frac{a}{y}+ \frac{b}{y} but this must be equal to \frac{x}{y} so we get \frac{x}{y}=\frac{a+b}{y}=\frac{  a}{y}+\frac{b}{y}

    If we DID allow \frac{1}{x}+\frac{1}{y}=\frac{1}  {x+y} then we would get nonsense like 2=1+1=\frac{1}{1}+\frac{1}{1}= \frac{1}{2} so 2= \frac{1}{2}
 
 
 
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