This seems to me to be an application of the difference of two squares:

(a * a - b * b) = (a + b)(a - b)

Substituting 1001 for a and 999 for b in the numerator gives us:

(1001 + 999) * (1001 - 999) = 2000 * 2 = 4000

We can make a similar substitution in the denominator and get:

(101 + 99) * (101 - 99) = 200 * 2 = 400

Simple division from there gives us 10.

jaroth04 wrote:This seems to me to be an application of the difference of two squares:

(a * a - b * b) = (a + b)(a - b)

Substituting 1001 for a and 999 for b in the numerator gives us:

(1001 + 999) * (1001 - 999) = 2000 * 2 = 4000

We can make a similar substitution in the denominator and get:

(101 + 99) * (101 - 99) = 200 * 2 = 400

Simple division from there gives us 10.

Yup right on. If you were writing it out, you could cancel out the "2"s and two zeroes, leaving 20/2 = 10, instead of calculating numerator and denominator (assuming you would write those out as well).