The numerator of a fraction is 2 less than its denominator. If 3 is added to each of the numerator and the denominator, the fraction increases by 1/18. Find the fraction.

Asked by khushdab | 1st Apr, 2020, 11:21: AM

Expert Answer:

Let the denominator of the required fraction be x.
→ Numerator will be x - 2.
According to the condition,
begin mathsize 16px style fraction numerator straight x space minus space 2 space plus 3 space over denominator straight x space plus 3 end fraction equals fraction numerator straight x minus 2 over denominator straight x end fraction plus 1 over 18
rightwards double arrow fraction numerator straight x space plus 1 over denominator straight x plus 3 end fraction minus fraction numerator straight x minus 2 over denominator straight x end fraction equals 1 over 18
rightwards double arrow straight x squared space minus 3 straight x space minus 108 equals 0
rightwards double arrow straight x squared space minus 12 straight x space plus space 9 straight x minus 108 equals 0 end style
→ (x-12)(x+9)=0

→ x = 12 or x = -9
 
Therefore, the required fraction is 10/12 or -11/-9= 11/9.

Answered by Yasmeen Khan | 1st Apr, 2020, 03:40: PM