Question

does anyone know how to simplify complex fractions?! D:

Answer 1

If you have something like \[\frac{a}{b+ic}\] typically you multiply the numerator and denominator by the complex conjugate:
\[\frac{a}{b+ic}\cdot \frac{b-ic}{b-ic}=\frac{ab-iac}{b^2+c^2}=\frac{ab}{b^2+c^2}-i\frac{ac}{b^2+c^2}\] So you easily get the regular form "\(x+iy\)" since \(a,b,c \in \mathbb{R}\)

Answer 2

more like this @kirbykirby

Answer 3

Oh sorry. The word "complex" in math has a very specific meaning (in higher mathematics). I'm sorry for that lol. What I did is beyond your level :S I'll explain what to do in your case:

Answer 4

thank you!

Answer 5

If you generally have two fractions, and want to divide them, like say:
\[\frac{a}{b} \div \frac{c}{d}\] Then you just change the \(\div\) and change it to \(\times\) and flip the second fraction. Thus giving \[\frac{a}{b} \times \frac{d}{c}= \frac{ad}{bc} \]

Notice that you can write the division of two fraction this way:
\[ \frac{a}{b} \div \frac{c}{d} =\frac{\frac{a}{b}}{\frac{c}{d}}\]

So in your case, just imagine
\(a =x+6\)
\(b=12\)
\(c=x-8\)
\(d=10\)

So you can re-write what you have in terms of two multiplying fractions

Answer 6

When you divide flip the divisor and multiply!

Answer 7

divide fractions* I should specify

Answer 8

\[\frac{x+6}{12}\div \frac{x-8}{10} \]... and there is not much left to do from here :)

Answer 9

thank you guys!