x2 + 2x + 7 x + 2
__________ = _____
x2+ 3x + 5 x + 3
In the conventional method we proceed as
x2 + 2x + 7 x + 2
__________ = _____
x2 + 3x + 5 x + 3
(x + 3) (x2 + 2x + 7) = (x + 2) (x2 + 3x + 5)
x3 + 2x2 + 7x + 3x2 + 6x + 21 = x3 + 3x2 + 5x + 2x2 + 6x + 10
x3 + 5x2 + 13x + 21 = x3 + 5x2 + 11x + 10
Canceling like terms on both sides
13x + 21 = 11x + 10
13x – 11x = 10 – 21
2x = -11
x = -11 / 2
Now we solve the problem using anatyayoreva formula.
x2 + 2x + 7 x + 2
__________ = _____
x2 + 3x + 5 x + 3
Consider
x2 + 2x + 7 x + 2
__________ = _____
x2+ 3x + 5 x + 3
Observe that
x2 + 2x x (x + 2) x + 2
______ = ________ = _____
x2+ 3x x (x + 3) x + 3
This is according to the condition in the sutra. Hence from the sutra
x + 2 7
_____ = __
x + 3 5
5x + 10 = 7x + 21
7x – 5x = -21 + 10
2x = -11
x = -11 / 2
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