Solve the equation frac{p + q - x}{r} + frac{ | vedclass

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(A) Given the equation: $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{4x}{p + q + r} = 0$.Add $1$ to each of the first thre

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$x = p + q + r$

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(A) Given the equation: $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{4x}{p + q + r} = 0$.Add $1$ to each of the first three terms to simplify:$(\frac{p + q - x}{r} + 1) + (\frac{q + r - x}{p} + 1) + (\frac{r + p - x}{q} + 1) + \frac{4x}{p + q + r} - 3 = 0$$\frac{p + q + r - x}{r} + \frac{q + r + p - x}{p} + \frac{r + p + q - x}{q} + \frac{4x - 3(p + q + r)}{p + q + r} = 0$$(p + q + r - x) (\frac{1}{r} + \frac{1}{p} + \frac{1}{q}) + \frac{4x - 3(p + q + r)}{p + q + r} = 0$Alternatively,rewrite the equation as:$(\frac{p + q - x}{r} + 1) + (\frac{q + r - x}{p} + 1) + (\frac{r + p - x}{q} + 1) + \frac{4x}{p + q + r} - 3 = 0$$(p + q + r - x) (\frac{1}{p} + \frac{1}{q} + \frac{1}{r}) = 3 - \frac{4x}{p + q + r}$$(p + q + r - x) (\frac{1}{p} + \frac{1}{q} + \frac{1}{r}) = \frac{3(p + q + r) - 4x}{p + q + r}$Setting $(p + q + r - x) = 0$ gives $x = p + q + r$.

Solve the equation $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{4x}{p + q + r} = 0$.

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