Question

The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity. The fraction is​

Answer 1

Answer:

3/5

Step-by-step explanation:

Let numerator=x

then denominator=x+2

so fraction=x/x+2

If 5 are added to the numerator then

Fraction=x+5/x+2=x/(x+2)+1

x+5=x+x+2

x-2x=2-5

-x=-3

x=3

So numerator=3

denominator=3+2=5

So the fraction=3/5

Answer 2

In the above Question , the following information is given -

The denominator of a fraction exceeds the numerator by 2. If 5 be added to the numerator the fraction increases by unity.

To find - The Required fraction

Solution -

The denominator of a fraction exceeds the numerator by 2.

Let the numerator of the fraction be x

Therefore denominator of the fraction is x + 2 .

So , the required fraction becomes [ x ] / [ x + 2 ]

Now , 5 is added to the Numerator of the fraction ...

So , the new numerator becomes [ x + 5 ]

Thus the new Fraction becomes -

[x + 5 ] / [ x + 2 ]

This is greater than the original fraction by unity

So ,

[ x ] / [ x + 2 ] + 1 = [x + 5 ] / [ x + 2 ]

[x + x + 2 ] / [ x + 2 ] = [ x + 5 ] / [ x + 2 ]

=> [ 2x + 2 ] / [ x + 2 ] = [ x + 5 ] / [ x + 2 ]

=> 2x + 2 = x + 5

=> x = 3

Required fraction = 3/5