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A fraction is such that the numerator is 2 less than the denominator. If yo

A fraction is such that the numerator is 2 less than the denominator. If you add 3 to the numerator and 5 to the denominator, the resulting fraction is equivalent to the original fraction. Find the fraction.

1 Answer

Let the denominator of the fraction be x 
Numerator is 2 times less than denominator. Therefore The fraction we get is -
After adding 3 to numerator and 5 to the denominator resulting fraction is equals to the original fraction -
therefore - 
x-2+3/x+5 = x-2/x
x+1/x+5 = x-2/x
Now by cross multiplication
(x+1)(x) = (x-2)(x+5)
x^2 + x = x^2 + 5x - 2x - 10 
x = 5x - 2x - 10
x = 3x - 10 
x - 3x = -10
-2x = -10
x = -10/-2
x = 5 
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