Question

The numerator of a fraction is one more than the denominator. if the numerator and the denominator are both increased by two, the new fraction will be one over four lessthan the original fraction. find the original fraction

Answer 1

Let the denominator be x
:- the numerator = x+1

Original fraction = (x+1)/x

New fraction = (X+1+'2')/(x+'2')

'2' this shows the factor which the numerator and the denominator is increased..

(X+1+2)/(x+2) = 1/4 + (x+1)/x

x+1 1 x+3
--------- = - - - + - - - -
x 4 x+2


x+1 (x+2) + 4(x+3)
------ = - - - - - - -------
x 4(x+2)

Cross multiply..



(x+1)(4x+8) = (x)[x+2+4x+12]

4x²+12x+8 = x(5x+14)

4x²+12x+8 = 5x²+14x

5x²- 4x²+14x-12x-8=0

x²+2x-8=0

x²+4x-2x-8=0

x(x+4)-2(x+4)=0

(x-2)(x+4)=0

:- x=2 or - 4

Recall that the original fraction = (x+1)/x

When x=2
The fraction = (2+1)/2 = 3/2