How To Add Fractions With Variables And Exponents

alright: in this video i'm gonna do an example of rewriting complex fractions and there's two different ways that you cango about simplifying complex fractions and again it's just a complex fractionall that is is you know you got a big fraction and then within that you have even morefractions is the basic idea so

How To Add Fractions With Variables And Exponents, again two ways to do 'em one way is tolook at all the denominators and you can multiply the top and bottomby the least common multiple of the of the denominators and the ideasthat'll get rid of everything except for it you know theone big attraction

another thing is to simply write thenumerator as a single fraction and the denominators a single fractionand then we're gonna do you is just use that the trick that we can flip and multiplyand that's how i've always done so that's how i'm gonna do this example and the others as wellso we have 2 over "x" plus three divided by 1 plus 3 divided by "x" you can think about the wine is beingone divided by one and again what i want to do is thenumerator is already a single fraction

i'm gonna write the denominator also isa single fraction so in this case i look at the denominatorswe have 1 and "x" so to get a common denominator i couldmultiply the first term a by "x" over "x" and in the numeratorwill simply leave that alone 2 over x+3 and then and the denominator we would havex over x plus three over x and again the the whole reason we we did that is sothat we could write the denominators a single fraction

so often times all you can skip this stepso in the numerator of the denominatorwe would have x +3 which we can't really do much withdivided by our common denominator of x so this is kinda the first half but getting the numeratorsingle fraction and now the denominator as a singlefraction and remember the trick is if you have afraction divided by a fraction we leave the top fraction alone and wetake the denominator we flip it over but we turn it intomultiplication

okay so instead of divided by x plus three over x we're multiplying byx-over x plus three and in this case on you know if there is anything to you tofactor and cancel i would certainly try to factor incancel but in this case in the numerator wehave a 2 times an x in the denominator we have x plus three inx plus three i would probably rewrite this simply is2 x and then x plus 3 quantity squared

again you can multiply denominator outyou could foil it out x squared plus 6x plus 9 but i think my own personal preference would againjust to be leave it in this nice factored form