What is the answer to this equation? 0 = - 300 + 200/(1-x) - 100/(1-x)?

Question

explainhow you reached you answer.

Answer 1

0 = - 300 + 200/(1-x) - 100/(1-x)
0= -300 +100/(1-x)
100/(1-x) = 300
multiply by 1-x
100 = 300(1-x)
1-x = 100/300 = 1/3
x=1-1/3
x=2/3 .

Answer 2

Start by getting a common denominator of (1-x) for each fraction. In other words, multiply the -300 by (1-x)/(1-x)

This gives you
-300 (1-x) ... 200 ... 100
------------- + ------ - ------- = 0
..... (1-x) ......(1-x) . (1-x)

Now combine the numerators:
-300 (1 - x) + 200 - 100
------------------------------- = 0
................ (1 - x)

Now multiply by (1 - x), not this will make the denominator disappear. By definition, x can't equal 1 or else your original equation would be wrong, so we don't have a problem doing this:

-300(1 - x) + 200 - 100 = 0
-300 + 300x + 100 = 0
-200 + 300x = 0
300x = 200
x = 2/3

As a double check:
-300 + 200 / (1 - (2/3)) - 100 / (1 - (2/3)) = ?
-300 + 200 / (1/3) - 100 / (1/3) = ?
-300 + 200 * 3 - 100 * 3 = ?
-300 + 600 - 300 = 0 <-- check

So the answer is x = 2/3