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How would I reduce this fraction?

$\frac{km+kn}{n^2+nm}$

I think it would be $\frac{2k}{n^2}$ but I am not sure.

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    @TonyK Sorry, the OP had half uppercase and half lowercase. Lowercase just looked better to me.2012-06-07

2 Answers 2

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$\frac{KM+KN}{N^2+NM}=\frac{K(M+N)}{N(N+M)}=\frac{K}{N}$

As Alex Jordan comments, we can cancel out $M+N$ if and only if $M+N\neq 0$. In this case, given the fact that the denominator is of the form $N(M+N)$ we already know this is a non-zero number, and we can cancel.

On the other hand, if we were given something like $x=y$ then either $x=y=0$ or $x\neq 0$ and then we can divide by $x$ and have $\frac yx=1$.

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    @DonAntonio I think my point is that it would be wrong to write statements like $\frac{ab}{2b}=\frac{a}{2}$. The RHS makes sense for $b=0$ but the LHS implicitly remains undefined for $b=0$. So the reader should be explicitly told to exclude $b=0$ from the RHS, leaving the expression undefined as it was in the LHS.2012-06-08
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$\frac{km+kn}{n^2+nm}=\frac{k(m+n)}{n(n+m)}=\frac{k}{n}$