Question 240675
p - (pd) = n


this is equivalent to:


p - (p*d) = n


factor out the p to get:


p*(1-d) = n


divide both sides by (1-d) to get:


p = n/(1-d)


go back to your original equation and replace p with n/(1-d) and you should get an identity equation.


your equation is:


p - pd = n


substitute n/(1-d) for p to get:


n/(1-d) - (n/(1-d)*d = n


multiply both sides of the equation by (n-d) to get:


n - n*d = n*(1-d)


remove parentheses to get:


n - n*d = n - n*d


that's your identity equation so the value you calculated for p is good.


another way to check is the let n = any number and d equal any number and solve for p.


let n = 2 and d = 3


p = n/(1-d) becomes p = 2/(-2) = -1


substitute for p = -1 and n = 2 and d = 3 in your original equation.


p - (pd) = n becomes:


-1 - (-1*3) = 2 which becomes -1 - (-3) = 2 which becomes -1 + 3 = 2 which becomes 2 = 2 which is true so the value for p is good.