How do you write a complex fraction that when simplified results in 1/x?
Follow the intuition below to get an answer, but one sample solution is
A complex fraction involves having two fractions inside one. Keeping this in mind, all you need to do is put together expressions that give you the above.
Here's the approach I'd suggest:
Note that dividing two fractions is the same thing as multiplying by the reciprocal. So say your complex fraction is
This makes things slightly easier to look at.
Now, you know that the numerator of your resulting fraction must equal 1. So, the best course of action is to set
Next, you know that the denominator of the resulting fraction must equal
You see that the
Hope that helped :)