does 84/84-x = 1 - (84)/x?

looks like 2 different questions, so as I understand them I will answer:

problem 1.

(84/84) - x = 1 - 84/x

84/84 = 1, so we subtract 1 from both side of equation:

-x = -84/x, here we divide both sides by -x

x/x = 84, since x/x can only equal 1, this can not be a solution.

problem 2.

x/(x+y) = 1/(1+y) you left the brackets out, which is why it was necessary to further elaborate.

First thing is to divide both sides by x

then you have 1/(x+y) = 1/(x(1+y))

then we can loose the numerator, by multiplying both sides by the denominators to show:

x+y = x(1+y) then multiply out to show:

x+y = x+xy subtract x from both sides

y = xy divide both sides by y

1 = x, so this does work.

Dear Asker,

There is a rule that the order of actions in mathematics calculation is that division and multiplication are done before adding and subtracting. Hence: 84/84-x is actually 1-x.

It might be that you mean there is a long division line - so it's actually 84/(84-x) - if that is the case, it should be solved as 1/(84/84-x/84) = 1/(1-x/84)

Same goes for the next expression: the you describe it is correct, but if it's the same as the above expression, you might mean x/(x+y) which is not 1/(1+y). A solution might be 1/(1+y/x).