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Simplifying Complex Fractions  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel 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 x2 the denominator gets flipped and then turned into multiplication that's 4 over 7, so this particular expression we can actually cancel out x2 we can factor the numerator over here this numerator turned into x2, x+2 and then we can cancel the x2. 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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Carl Horowitz
B.S. in Mathematics University of Michigan
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Simplifying Complex Fractions
Problem 1 9,801 viewsSimplify:
1 + 1 a b 1 − 1 a² b² 
Simplifying Complex Fractions
Problem 2 7,527 viewsSimplify:
3x⁻¹ − 3y⁻¹ y⁻² − x⁻² 
Simplifying Complex Fractions
Problem 3 1,735 views 
Simplifying Complex Fractions
Problem 4 1,268 views 
Simplifying Complex Fractions
Problem 5 1,352 views 
Simplifying Complex Fractions
Problem 6 1,112 views
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