Question 1006126
start with 1/a + 1/p = 1
multiply both sides of the equation by ap to get:
p + a = ap
subtract a from both sides of the equation to get:
p = ap - a
factor out the a to get:
p = a * (p-1)
divide both sides of the equation by (p-1) to get:
p / (p-1) = a
your solution is:
a = p / (p-1)


confirm by taking any value of p at random and solving for a.


note that this assumes that p is positive.


it gets more complex if you assume that a or p or both can be negative.


i don't think that they wanted it to be that complex for you so i'll assume a and p are both positive.


we have a = p/(p-1)


assume any positive value for p.


we'll try 555.


a is equal to 555/554.


1/a + 1/p = 1 becomes:


1/(555/554) + 1/555 = 1.


since 1/(555/554) is the same as (554/555), the equation becomes:


554/555 + 1/555 = 1 which becomes 555/555 = 1 which becomes 1 = 1.