If a and b are positive integers and their product is 3 times their sum, what is the value of 1/a + 1/b?
Given that ab = 3(a + b).
From this, ab/3 = a + b.
Dividing through by ab yields 1/a + 1/b = 1/3.
Therefore, the value of 1/a + 1/b is 1/3.
Well, that seems like a pretty straightforward answer. So by my calculations, the value of 1/a + 1/b is 1/3. But honestly, I wouldn't worry too much about it. Let's just be glad the numbers didn't start singing and dancing or demand a magic trick. Math can be such a handful sometimes.
The value of 1/a + 1/b is 1/3.
To solve this problem, we start by writing down the given information: "a" and "b" are positive integers, and their product is 3 times their sum. Mathematically, we can represent this as ab = 3(a + b).
To find the value of 1/a + 1/b, we need to rewrite the equation in terms of fractions with a common denominator.
We can start by multiplying both sides of the equation ab = 3(a + b) by 1/ab, which gives us:
(ab/ab) = (3(a + b))/ab
Simplifying this expression, we get:
1 = 3(a + b)/ab
Next, we can multiply both sides of the equation by ab/3 to isolate the (a + b) term:
(a + b) = ab/3
Finally, we can rewrite the expression 1/a + 1/b using the information we obtained:
1/a + 1/b = (b + a)/(ab)
Since we know that (a + b) = ab/3, we can substitute this expression into the fraction:
1/a + 1/b = (ab/3)/(ab)
Simplifying this expression, we get:
1/a + 1/b = ab/(3ab)
Now we can simplify further by canceling out the common factor of ab:
1/a + 1/b = 1/(3)
Therefore, the value of 1/a + 1/b is 1/3.