Question 52067
1) {{{p = (r-1)/r}}}
2) {{{p/(p+1) = r}}}

Let's solve equation 2) for p and see if it matches equation 1).

2) {{{p/(p+1) = r}}} Multiply both sides of the equation by (p+1).
2a){{{p = r(p+1)}}} Apply the distributive property to the right side.
2b){{{p = rp+r}}} Subtract rp from both sides.
2c) {{{p-rp = r}}} Simplify this by factoring out the p on the left side.
2d) {{{p(1-r) = r}}} Now divide both sides by (1-r).
2e) {{{p = r/(1-r)}}} You can rewite this as:
2f) {{{p = -r/(r-1)}}} Now compare this with equation 1)
1) {{{p = (r-1)/r}}}

You can see that equation 2f) is the negative reciprocal of equation 1) so Peter is incorrect in his statement.