SOLUTION: x/a+x/b=c multiply both sides by ab/1 xb +xa =cab divide both sides by b+a i have x+x =cab/b+a but answer in book says x= cab/a+b what am i missing

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: x/a+x/b=c multiply both sides by ab/1 xb +xa =cab divide both sides by b+a i have x+x =cab/b+a but answer in book says x= cab/a+b what am i missing      Log On


   

Question 715042: x/a+x/b=c multiply both sides by ab/1 xb +xa =cab divide both sides by b+a i have x+x =cab/b+a but answer in book says x= cab/a+b what am i missing
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is that you crossed out the same numbers in numerator and denominator in a careless way, without thinking of what it meant. and that was a mistake).
Unfortunately we all make silly mistakes on a daily basis,
and I have found that whatever mistake I make,
I cannot notice when I check my work.

x%2Fa%2Bx%2Fb=c --> xb%2Bxa=cab (multiplying both sides times ab ) is correct.
Dividing xb%2Bxa by %28b%2Ba%29 you should do
%28xb%2Bxa%29%2F%28b%2Ba%29=x%28b%2Ba%29%2F%28b%2Ba%29 (taking out x as a common factor)

The "crossing out" of factors that you can do afterwards is based on what you know of multiplication of fractions.
You are "un-multiplying" out a factor equal to 1:
x%28b%2Ba%29%2F%28b%2Ba%29=%28x%2F1%29%28%28b%2Ba%29%2F%28b%2Ba%29%29=%28x%2F1%29%2A1=x
You might write it as
or even shorter.
The crossing out of that %28b%2Ba%29 that was a factor of the whole numerator and a factor of the whole denominator means "un-multiplying" that 1-in-disguise factor %28b%2Ba%29%2F%28b%2Ba%29 and then eliminating it as we realize that multiplying times 1 does not change anything.
Your teacher may say that you can only cross out a factor that is in numerator and denominator if it is a factor of the whole numerator and also a factor of the whole denominator.

That is not a "rule" for magical crossing out to be memorized.
It stems from what every fourth grader should know and remember for life.
In math, all you need to memorize is the meaning of symbols and names used (like what an exponent means, and what we mean by "common denominator).
That is vocabulary.
You also need to remember some "grammar of algebra rules," agreed by convention and known as "order of operation" rules.
Beyond that you pick up some tricks from other people here and there.
Maybe you can even discover new tricks for easier problem solving that other people will copy later.

When you "divided" piecemeal to get x%2Bx, it was as if
you were equating %28xb%2Bxa%29%2F%28b%2Ba%29 with xb%2Fb%2Bxa%2Fa=x%2Bx
But %28xb%2Bxa%29%2F%28b%2Ba%29 does not equal xb%2Fb%2Bxa%2Fa
because we do not add fraction by adding numerators and adding denominators separately.
Otherwise we would add 1%2F2%2B1%2F3 to get 2%2F5
We go though the trouble of finding a common denominator.