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Simplifying Complex Fractions - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Simplifying rational expressions combines everything learned about factoring common factors and polynomials. When simplifying complex fractions, factor the numerator and denominator into terms multiplying each other and look for equivalents of one (something divided by itself). Include parenthesis around any expression with a "+" or "-" and if all terms cancel in the numerator, there is still a one there.

Simplifying complex fractions, so a complex fractions is a fraction where we actually have more than one fraction involved so we're used to just a simple 3 over 5 or just one thing in the top one thing in the bottom. Well complex fraction is, is throwing in an extra fraction so in this case both are numerator and denominator our fractions. We don't need both if we just had one it still would be a complex fraction and how we solve this is basically by flipping the denominator and then multiplying, so you know this one from just basic complex fractions. This just turned into 3 over 5 flip our denominator and it turned into multiplication so this is just then 7 over 9. We can cancel the 3 and the 9 so that it becomes a 3 and then just multiply across so this turns into a 1 one times 7 is 7, 5 times 3 is 15.
Okay, this one we are dealing with rational expressions so we actually have fractions and x's and all that stuff in there the same exact rule still holds you have a fraction at the top fraction at the bottom just flip and multiply, so the numerator stays the same x-2 the denominator gets flipped and then turned into multiplication that's 4 over 7, so this particular expression we can actually cancel out x-2 we can factor the numerator over here this numerator turned into x-2, x+2 and then we can cancel the x-2. Okay multiplying across we then end up with 3 times x+2 all over 7. Okay you could distribute this 3 through if you wanted you don't have to this answer would typically be perfectly acceptable so whenever we have a single fraction over a single fraction is called a complex fraction and we saw what as we were doing any other type of number.

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