Question

. The numerator of a fraction is 2 less than the denominator. If 5 is added to both
3
the numerator and the denominator, the fraction becomes Find the fraction.
4
A
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Answer 1

Answer:

Step-by-step explanation:

Let a/b is the fraction

so a+2=b

(a+5)/b=1+(a/b)

or (a+5)/(a+2)=1+{a/(a+2)}

or, (a+5)/(a+2)=(a+2+a)/(a+2)

or , (a+5)(a+2)=(a+2)(2a+2)

or, (a+5)(a+2)-(a+2)(2a+2)=0

or, (a+2)(a+5–2a-2)=0

or, (a+2)(3-a)=0

if a+2=0 , then a=-2 ,and b=a+2=-2+2=0

if 3-a=0 , then a=3 , and b=a+2=3+2=5

fraction a/b=-2/0 and 3/5

-2/0 is not a fraction

so the fraction is 3/5

SHORT CUT METHOD :—

As , if we add 5 to the numerator the fraction increases by unity , so dinominator of the fraction must be 5 , as 5/5=1 , as numerator is 2 less than dinominator , so numerator =5–2=3 ,

So fraction is 3/5 ans