An abstract representation of the mathematical concept described. Visualize a large number 9, signifying the quotient suggested, in the center of the image. Surrounding the number 9, illustrate two consecutive numbers, symbolized by a pair of adjacent spheres. Represent the concept of division with a stylized slash or dividing line, placed between these elements. Finally, visualize the positive difference between the two numbers with a scale in equilibrium, indicating balance. The visual ingredients, the consecutive numbers, the division sign, the number 9, and the balanced scale, should blend in an appealing manner. Ensure the image does not contain any text.

The sum of two consecutive numbers divided by their positive difference is equal to 9. Find the largest number.

or

n + n-1 = 9
2 n = 10
n = 5
same old boring solution :)

the difference between any two consecutive numbers is just 1.

so, x + x+1 = 9
x = 4
the next number is 5

or, following the wording:

(x + x+1)/(x+1 - x) = 9

2x +1 = 9
x = 4

same old

Thanks for the explanation

Why did the two consecutive numbers go to therapy? Because they couldn't find a positive difference between them!

Now, let's solve this riddle. Let's call the larger number "x" and the smaller number "x-1", since they are consecutive. According to the problem, (x + (x-1))/(x - (x-1)) = 9.

Simplifying this expression, we get:
(2x - 1)/(1) = 9

If we multiply both sides by 1, we get:
2x - 1 = 9

Now, let's add 1 to both sides:
2x = 10

Dividing both sides by 2, we find:
x = 5

So, the largest number is 5.

To solve this problem, let's first set up the equations based on the given information.

Let's assume the first consecutive number is x. Since the numbers are consecutive, the second number will be x + 1.

The sum of two consecutive numbers is x + (x + 1).

The positive difference between two consecutive numbers is |x - (x + 1)|, which simplifies to 1.

According to the given information, the sum divided by the positive difference is equal to 9:

(x + (x + 1))/1 = 9

Now, let's simplify the equation:

2x + 1 = 9
2x = 8
x = 4

So, the first consecutive number is 4.

Since the second consecutive number is x + 1, the largest number will be 4 + 1 = 5.

Therefore, the largest number is 5.