Question

Make x the subject of the formula


`r = \sqrt{ (ax - p)/(q + bx) }`

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Answer 1

`\boxed{x = \frac{p + q {r}^(2) }{a - b {r}^(2) } }`

Explanation:

`Solve \: for \: x: \\ = > r = \sqrt{ (ax - p)/(q + bx) } \\ \\ </p><p>r = \sqrt{ (ax - p)/(q + bx) } \: is \: equivalent \: to \: \sqrt{ (ax - p)/(q + bx) } = r :\\ = > \sqrt{ (ax - p)/(q + bx) } = r \\ \\ Raise \: both \: sides \: to \: the \: power \: of \: two: \\ = > (ax - p)/(q + bx) = {r}^(2) \\ \\ Multiply \: both \: sides \: by \: (q + b x): \\ = > ax - p = {r}^(2) (q + bx) \\ \\ Expand \: out \: terms \: of \: the \: right \: hand \: side: \\ = > ax - p = q {r}^(2) + b {r}^(2)x \\ \\ Subtract \: b {r}^(2)x - p \: from \: both \: sides: \\ = > x(a - b {r}^(2) ) = p + q {r}^(2) \\ \\ Divide \: both \: sides \: by \: a - b {r}^(2) : \\ = > x = \frac{p + q {r}^(2) }{a - b {r}^(2) }`