what is the technique when solving complex fractions?
a
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1 - 1
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1+ 1
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a-1
Hello 21_knipIf I read your attachment correctly, start with the 1 and the fraction at the bottom first, and write them over a common denominator; like this:
$\displaystyle 1 + \frac{1}{a-1} = \frac{a-1}{a-1}+\frac{1}{a-1}$
$\displaystyle = \frac{a-1+1}{a-1}$
$\displaystyle = \frac{a}{a-1}$
You now need 1 over this answer; that's $\displaystyle \frac{1}{\frac{a}{a-1}}$
This is simply the reciprocal of the fraction: turn it 'upside-down': $\displaystyle \frac{a-1}{a}$
Now you do a similar thing for the remaining 1 and this new fraction:
$\displaystyle 1 - \frac{a-1}{a} = \frac{a}{a} - \frac{a-1}{a}$
$\displaystyle = \frac{a-a{\color{red}+}1}{a}$ Watch that sign!
$\displaystyle = \frac{1}{a}$
And so finally (as chiph588@ said) invert and mulitply:
$\displaystyle \frac{a}{\frac{1}{a}}$
$\displaystyle = a \times \frac{a}{1}$
$\displaystyle = a^2$
I hope you followed all that.
Grandad