Question

The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2, the fraction is increased by 1/12 .Find the original fraction.

Answer 1

Step-by-step explanation:

Denominator = x

Numerator = x - 1

fraction = x - 1 / x

According to Question

(x-1)/x + 1/12 = (x+1)/(x+2)

(12(x-1)+x)/12x = (x+1)/(x+2)

(13x-12)/12x = (x+1)/(x+2)

(13x-12)(x+2)=12x(x+1)

13x² + 26x - 12 x - 24 = 12x² + 12x

13x² + 14x - 24 = 12x² + 12x

x² + 2x - 24 = 0

x² + 6x - 4x - 24 = 0

x ( x + 6 ) - 4 ( x + 6 ) = 0

( x + 6 ) ( x - 4 ) = 0

x = - 6 or x = 4

Neglecting negative number we assume x = 4

Therefore, Denominator = 4 & Numerator = 3

Fraction = 3/4 ....

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