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Help finding least common denominators.Numerator on both is one, Demi are x+5 and x-6.

Help finding least common denominators.Numerator on both is one, Demi are x+5 and-example-1
User RoboYak
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1 Answer

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(x+5)(x-6)

1) Considering that we have these two rational expressions:


(1)/(x+5)+(1)/(x-6)

2) Since we have two different denominators, x+5 and x-6 then the least common denominator will be a simple product between them in this case:


\begin{gathered} (1)/(x+5)+(1)/(x-6)= \\ (1(x-6)+1(x+5))/((x+5)(x-6))= \\ (x-6+x+5)/((x+5)(x-6))= \\ \frac{2x-1}{{\color{Red} (x+5)(x-6)}} \end{gathered}

Note that after writing the Least Common Denominator (x-5)(x+6) we divide this by each original denominator and then multiply by the original numerator: 1 and then we add them up both.

3) Hence the least denominator is (x+5)(x-6) in red.

User Fluidbyte
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