Question

Simplifying Complex Rational Expressions.
Hello, I understand this concept to some extent, but I just can't figure out this problem. It says the answer is (13-x)/(x+2)(x-5) but I don't see how to do this. It is way too complicated to type so it's in the screenshot

Answer 1

First, subtract the fractions in the numerator of the complex fraction, and add the fractions in the denominator of the complex fraction.

Answer 2

Once you have a complex fraction of just a fraction over a fraction, then divide the fractions by multiplying the fraction in the numerator by the reciprocal of the fraction in the denominator.

Answer 3

(13-x)/(x-6)(x+2)
------Complex-----
(-5+x)/(x-6)

Answer 4

Ok I have finished it. I understand now. Thank you!!!

Answer 5

I would have never figured it out on my own without you getting me started in the right direction!

Answer 6

(Please don't delete what you're saying or anything because it might be good stuff that will help me later)

Answer 7

\(\Large \dfrac{\frac{7}{x^2 - 4x - 12} - \frac{1}{x + 2} }{ \frac{1}{x - 6} + 1 } =\)

\(\Large =\dfrac{\frac{7}{(x - 6)(x + 2)} - \frac{1}{x + 2} }{ \frac{1}{x - 6} + \frac{x - 6}{x - 6} } \)

\(\Large =\dfrac{\frac{7}{(x - 6)(x + 2)} - \frac{x - 6}{(x - 6)(x + 2)} }{ \frac{1}{x - 6} + \frac{x - 6}{x - 6} } \)

\(\Large =\dfrac{\frac{7 - x + 6}{(x - 6)(x + 2)} }{ \frac{1 +x - 6}{x - 6} } \)

\(\Large =\dfrac{\frac{- x + 13}{(x - 6)(x + 2)} }{ \frac{x - 5}{x - 6} } \)

Answer 8

This is up to what you did above. You are correct so far.
Now we divide the numerator by the denominator.

Answer 9

\(\Large =\dfrac{\frac{- x + 13}{(x - 6)(x + 2)} }{ \frac{x - 5}{x - 6} } \)

\(\Large =\dfrac{- x + 13}{(x - 6)(x + 2)} \times \dfrac{x - 6}{x - 5} \)

\(\Large =\dfrac{(- x + 13)(x - 6)}{(x - 6)(x + 2)(x - 5)} \)

\(\Large =\dfrac{(- x + 13)\cancel{(x - 6)}}{\cancel{(x - 6)}(x + 2)(x - 5)} \)

\(\Large =\dfrac{- x + 13}{(x + 2)(x - 5)} \)

\(\Large =\dfrac{13 - x}{(x + 2)(x - 5)} \)

Answer 10

Is that what you got?

Answer 11

Yep! Thank you and sorry for replying late.

Answer 12

You're welcome.