Answer: [tex]x = \frac{mn(q - p)}{n-m}\\\\[/tex]
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Work Shown:
Part 1
[tex]\frac{x-m}{m} + p = \frac{x-n}{n} + q\\\\\frac{x-m}{m} - \frac{x-n}{n} = q - p\\\\\frac{n(x-m)}{mn} - \frac{m(x-n)}{mn} = q - p\\\\\frac{xn-mn}{mn} - \frac{xm-mn}{mn} = q - p\\\\\frac{xn-mn-(xm-mn)}{mn} = q - p\\\\[/tex]
Part 2
[tex]\frac{xn-mn-xm+mn}{mn} = q - p\\\\\frac{xn-xm}{mn} = q - p\\\\\frac{x(n-m)}{mn} = q - p\\\\x(n-m) = mn(q - p)\\\\x = \frac{mn(q - p)}{n-m} \\\\[/tex]
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Explanations:
- There are quite a bit of steps. I decided to break things into two parts.
- The goal is to get x all by itself on its own side, which is why I subtracted (x-n)/n from both sides in part 1, step 2. I also subtracted p from both sides.
- Afterward, I gave each fraction the LCD mn. I multiplied top and bottom of the first fraction by n/n. I did a similar operation to the second fraction, but with m instead.
- From there, we distribute and simplify. The mn terms cancel on the left side numerator (second step of part 2).
- The n≠m is there to prevent the denominator (n-m) from being zero. We cannot divide by zero.
- If the formulas don't properly display, then you might have to refresh the page.
