Marla Payton

Answered

2021-12-16

How to add two compound fractions with fractions in numerator like this one:

$\frac{\frac{1}{x}}{2}+\frac{\frac{2}{3x}}{x}$

or fractions with fractions in denominator like this one:

$\frac{x}{\frac{2}{x}}+\frac{\frac{1}{x}}{x}$

or fractions with fractions in denominator like this one:

Answer & Explanation

nghodlokl

Expert

2021-12-17Added 33 answers

One easy way to figure this out is that dividing by x is the same as multiplying by 1/x (but all bets are off when x=0, as division by 0 is undefined). So

$\frac{\frac{a}{b}}{c}=\frac{1}{c}\frac{a}{b}=\frac{a}{bc}$

$\frac{a}{\frac{b}{c}}=a\frac{1}{\frac{b}{c}}=a\frac{c}{b}=\frac{ac}{b}$

Dabanka4v

Expert

2021-12-18Added 36 answers

Let us start with the properties:

Division by a number or fraction is the same as multiplication by its inverse or reciprocal.

Division by r is equal to the multiplication by

Division by

Sum of fractions

Apply (1) to

and (2) to

So by (3) we have

For

We have

We can apply the property Division by a fraction is the same as multiplication by its inverse or reciprocal to the following fraction

RizerMix

Expert

2021-12-29Added 437 answers

Here is a start for the first one:

Now try to derive

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