Question

The numerator of a fraction is 1 less than its denominator if three is added to both numerator and denominator the fraction increased by 3/28 find the fraction

Answer 1

Let the numerator be x and denominator be y.

x=y-1 ----------(equation1)

x+3/y+3=x/y+3/28

x+3/y+3=28x+3y/28y

(28y)(x+3)=(28x+3y)(y+3)

28xy+84y=28xy+84x+3y^2+9y

84y-84x=3y^2+9y ----------- (equation2)

From equation1 put value of x in equation2

84y-84(y-1)=3(y^2+3y)

84y-84y+84=3(y^2+3y)

84=3(y^2+3y)

84/3=y^2+3y

28=y^2+3y

y^2+3y-28=0

y^2+7y-4y-28=0

y(y+7)-4(y+7)=0

(y+7)(y-4)=0

y=-7,4

If y=-7

then x=y-1

x=-7-1

x=-8

if y=4

then x=y-1

x=4-1

x=3

Therefore, the fraction can be -7/-8 or 4/3