Algebra i need solution help me ?

Question

solve for

a-b/ab+ b-c/bc + c-a/ac

need solution thanks

Answer 1

here how it goes:

first get their LCD. get their denominator which is abc. now, multiply the abc to each term. i'll do it one by one:

abc (a-b/ab) = c(a-b)/abc why? if you divide abc to ab, c will be left and ab will be cancelled. the c left will now be multiplied to the numerator but the LCD abc will remain as the denominator. then multiply c(a-b).

it will result to ac-bc then just copy the denominator abc so it will be ac-bc/abc.

same to do with the other two:

abc (b-c/bc) = a(b-c)/abc  = ab-ac/abc

abc (c-a/ac) = b(c-a)/abc = bc-ab/abc

now, as a rule in adding fractions, the fractions to be added must have the same denominator and then just add their numerator and copy the denominator. so, we already have fractions with the same denominator. we're just going to add their numerator:

ac-bc+ab-ac+bc-ab/abc

in adding, another rule that must be followed is combine like terms. so:

ac-ac-bc+bc+ab-ab/abc

notice that if we are going to add the terms whick are alike in the numerator it will leave as all zero result. so the numerator will be 0 then just copy the denominator which is abc so the answer is:

0/abc that will directly be 0 as a final answer.

Answer 2

Make the denominator abc (common) and then solve it.

= ac-bc +ab-ac+bc-ab /abc

= 0/abc

= 0

Answer 3

I presume you're expected to carry out the additions and subtractions.  The problem is that there's no way to tell from what you've typed exactly what the numerators and denominators are.  For instance, is that a - (b/ab) or (a - b)/ab?

I'm going to assume, from the symmetry, that your problem actually is

(a - b)/ab + (b - c)/bc + (c - a)/ac

If that's wrong, you'll need to post it again.

First off, you need a least common denominator.  Your LCD here will be abc - that being the simplest thing that has all of the factors in common.  To put the first fraction over that, we need to multiply by c/c.  For the second, multiply by a/a.  For the third, b/b.  So we end up with:

[c(a - b) + a(b - c) + b(c - a)]/abc

To simplify the numerator, carry out the multiplications and collect similar terms:

ac - bc + ab - ac + bc - ab = (ac - ac) + (-bc + bc) + (ab - ab) = 0 + 0 + 0 = 0

So we end up with 0/abc = 0, assuming none of a, b and c are also 0.

Again, if I've misread your problem, then this answer is wrong.  You'll need to post it again and clarify it.