Question

The denominator of a fraction exceeds its
numerator by 2. If one is added to both numerator
and denominator, the difference between new and
the original fraction is . Find the original
fraction with positive denominator. [4 Marks]​

Answer 1

Answer:

Let the denominator of a fraction be =x

let the numerator of a fraction be =x+3

required fraction=x+3/x

new fraction=x+3+1/x+1

=x+4/x+1

A/Q

x+3/x - x+4/x+1 =1/24

(x+3)(x+1)-(x)(x+4)/x(x+1)=1/24

x2+x+3x+3-x2-4x/x2+x=1/24

3/x2+x=1/24

3×24=x2+x

72=x2+x

0=x2+x-72

0=x2+9x-8x-72

0=x(x+9)-8(x+9)

0=(x+9)(x-8)

let x+9=0 and x-8=0

x= -9 and x=8

• •

• denominator can not be negative

•

• •denominator=x=8

and numerator=x+3=8+3=11

required fraction=11/8