SOLUTION: 1/a+1/p=1 solve for a

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Question 1006126: 1/a+1/p=1 solve for a
Found 3 solutions by Alan3354, josgarithmetic, Theo:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/a+1/p=1 solve for a
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1/a = 1 - 1/p = (p-1)/p
Invert
a = p/(p-1)

Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
a is in only one term , so isolate that term first.

1%2Fa=1-1%2Fp



1%2Fa=%28p-1%29%2Fp

a%281%2Fa%29=a%28p-1%29%2Fp

1=a%28p-1%29%2Fp

1%28p%2F%28p-1%29%29=a
OR
highlight%28a=p%2F%28p-1%29%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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.