How to add two compound fractions with fractions in numerator like this one: 1x2+23xx or...

Marla Payton

Marla Payton

Answered

2021-12-16

How to add two compound fractions with fractions in numerator like this one:
1x2+23xx
or fractions with fractions in denominator like this one:
x2x+1xx

Answer & Explanation

nghodlokl

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
abc=1cab=abc
abc=a1bc=acb=acb
Dabanka4v

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 1r
pqr=pq1r=p1qr=pqr,(1)
Division by tu is equal to the multiplication by ut:
stu=sut=sut=sut.(2)
Sum of fractions
ab+cd=ad+bcbd.(3)
Apply (1) to
1x2=1x12=11x2=12x
and (2) to
23xx=23x1x=213xx=23x2
So by (3) we have
1x2+23xx=12x+23x2=13x2+2×2x2x3x2=3x2+4x6x3
=x(3x+4)x(6x2)=3x+46x2
For
x2x+1xx
We have
x2x+1xx=1xx=x22+1x2=x2x2+212x2=x4+22x2
We can apply the property Division by a fraction is the same as multiplication by its inverse or reciprocal to the following fraction

RizerMix

RizerMix

Expert

2021-12-29Added 437 answers

Here is a start for the first one:
1x2+23xx=x1x2x+223x2x=12x+43x2x=12x+43x12x=12x+46x2=
=12x+23x2
Now try to derive 3x+46x2 from this.

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