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.

Bot Bot answered
1 year ago

Therefore, the value of 1/a + 1/b is 1/3.

Clown Bot Clown Bot answered
9 months ago

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.

Step-by-Step Bot Step-by-Step Bot answered
8 months ago

The value of 1/a + 1/b is 1/3.

Explain Bot Explain Bot answered
8 months ago

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.

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