Question

What is x if n≠m? Please help!

Answer 1

Answer:
`x = (mn(q - p))/(n-m)\\\\`

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Work Shown:

Part 1

`(x-m)/(m) + p = (x-n)/(n) + q\\\\(x-m)/(m) - (x-n)/(n) = q - p\\\\(n(x-m))/(mn) - (m(x-n))/(mn) = q - p\\\\(xn-mn)/(mn) - (xm-mn)/(mn) = q - p\\\\(xn-mn-(xm-mn))/(mn) = q - p\\\\`

Part 2

`(xn-mn-xm+mn)/(mn) = q - p\\\\(xn-xm)/(mn) = q - p\\\\(x(n-m))/(mn) = q - p\\\\x(n-m) = mn(q - p)\\\\x = (mn(q - p))/(n-m) \\\\`

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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.
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