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!
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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