MHB Simplifying compound fractions

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To simplify the compound fraction [1/(1+x+h) - 1/(1+x)] / h, finding a common denominator for the top two fractions is essential. The common denominator is (1+x+h)(1+x), allowing for the expression to be rewritten as [(1+x) - (1+x+h)] / [(1+x+h)(1+x)]. This results in a simplified numerator of -h, leading to the overall simplification of the compound fraction. The final expression can be further reduced by dividing by h, yielding -1/[(1+x+h)(1+x)]. Understanding how to manipulate common denominators is crucial in simplifying such fractions effectively.
datafiend
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Hi all,
I'm having a problem simplifying this:

[1/(1+x+h) - 1/(1+x)] / h

How do you get the common denominators for the top 2 fractions?

Thanks
 
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Maybe try to find a common denominator for 1+x+h and 1+x.

$(1+x+h)\times(1+h) = x^2+x(2+h)+1+h$
 
Last edited:
In the numerator, I would use:

$$\frac{1}{a}-\frac{1}{b}=\frac{b-a}{ab}$$
 
mark,
thanks again!
 

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