Determine the Number/Answer with Explanation

[Guest]

A number, to which 1/m th and 1/n th of itself is added, then a deducted, the result is b. Determine the number.

Answer given with problem:

(a + b)mn / mn + m + n.

Please explain how the answer was obtained.

[Stancho Pavlov]

[tex]x+\frac{x}{n}+\frac{x}{m} - a = b[/tex].
[tex]x= \frac{(a+b)mn}{mn+m+n}[/tex].

[Guest]

x + x/n + x/m - a = b. I understand this step.

x = (a + b)mn / mn + m + n. How did you get to this step ?

[Guest]

Please reply, Thanks.

[Guest]

x + x/n + x/m - a = b. I understand this step.
how to get to next step......not my post but here is one way to do it
Multiply across by "mn" ......

mnx + mx + nx = (a + b)mn

x(mn + m + n) = (a + b)mn

x = (a+b)mn /(mn + m + n)

[Guest]

x(mn + m + n) = (a + b)mn

" x(mn + m + n) = (a + b)mn

x = (a+b)mn /(mn + m + n) " I don't understand these steps.

[Guest]

" x(mn + m + n) = (a + b)mn

x = (a+b)mn /(mn + m + n) " I don't understand these steps....ANS >>>...ALL I DID WAS DIVIDE ACROSS BY (mn + m + n)

[Guest]

Ok, thanks.