How To Add Complex Fractions

- we want to simplify the given complex fraction. to do this, we'll first find the difference of the two rational expressions on top. and then since a fraction bar represents division, we'll then divide the difference by y,

How To Add Complex Fractions, which we can think of as y/1. so instead of dividing we'll end up multiplying by the reciprocal or 1/y. but for the first step, we want to find this difference,

so we must find a common denominator. so our first denominator is the quantity x + y and the second denominator is just x. so the least common denominator would be the product of these 2 or x x quantity x + y. which means this first fraction needs the factor of x, so we're going to multiply by x/x. and then for the second fraction, it's missing a factor of x + y,

so we'll multiply by the quantity x + y over the quantity x + y. so notice how on top we have a common denominator of x times the quantity x + y, and now we can combine the numerators. this first numerator is 2x. and then we'd have - 2 x the quantity x + y. this is still over y. and now we'll simplify this numerator

by clearing the parenthesis and combining like terms. so the denominator's going to stay the same. so now looking at the numerator we would have 2x, and now we'll distribute -2 because of the subtraction. so we'd have - 2x and then - 2y. well, 2x - 2x is 0, so this numerator simplifies to -2y. and now, again, because this larger fraction by represents division, we're going to write this as a division problem.

so we have the fraction on top -2y/x x the quantity x + y divided by y. and remember we can make y into a fraction by writing y as y/1. so instead of dividing by a fraction we normally multiply by the reciprocal. so this division problem is equivalent to -2y over x x the quantity x + y x the reciprocal of y/1, which would be 1/y. and now before we multiply,

we want to simplify out any common factors between the numerators and denominators that would simplify to 1. notice that we do have a factor of y over a factor of y that would simplify to 1, and unfortunately nothing else simplifies. so we have -2 x 1 that's -2, and our denominator is x x the quantity x + y. this would be the simplified form

of the given complex fraction. now, i do want to mention, if you have to enter this into an online homework system, we would have to include another set of parenthesis around the denominator. have to enter this into the computer as -2 divided by-- and then set a parenthesis for the denominator, i hope this example helps. â