Question

the numerator of a fraction is 2 less than the denominator.if 3 is added to both the numerator and denominator, the fraction becomes 3 by 4. find the fraction?
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Answer 1

Step-by-step explanation:

Let the original fraction be x/x+2

x+3/x+2+3=3/4

x+3/x+5=3/4

4 (x+3)=3 (x+5)

4x+12=3x+15

4x-3x=15-12

x=3

so the original fraction is

x/x+2=3/5

Answer 2

Given :

• The numerator of a fraction is 2 less than the denominator.
• If 3 is added to both the numerator and denominator the fraction becomes 3 by 4.

To find :

• The fraction.

According to the question,

Let the denominator be x

And numerator be x - 2

$\rightarrow \sf{ \frac{x - 2 + 3}{x + 3} = \frac{3}{4} }$

$\rightarrow \sf{ \frac{x + 1}{x + 3} = \frac{3}{4} }$

$\rightarrow \sf{3(x + 3) = 4(x + 1)}$

$\rightarrow \sf{3x + 9 = 4x + 4}$

$\rightarrow \sf{3x - 4x = 4 - 9}$

$\rightarrow \sf{ \cancel - \: x = \cancel- \: 5}$

$\therefore \sf \red{x = 5}$

________________....

Numerator is x - 2

→ 5 - 2

→ 3

_______________....

Denominator is x

→ 5

_______________....

So,the fraction is $\sf{ \frac{3}{5} }$