Question

The numerator of a fraction is 3 less than the denominator.If the numerator and denominator are both increased by 2 , the new fraction becomes 6/7 . Find the original fraction

Answer 1

let x = the denominator
let x-3 = the numerator (3 less than the denominator) 

the fraction is: 

(x-3) / x 

increasing the numerator and the denominator by 1 makes your fraction equal to 3/4 

your equation for this is: 

(x-2) / (x+1) = 3/4 

multiply both sides of this equation by (x+1) to get: 

(x-2) = (3/4) * (x+1) 

multiply both sides of this equation by 4 to get: 

4 * (x-2) = 3 * (x+1) 

simplify to get: 

4x - 8 = 3x + 3 

subtract 3x from both sides of this equation and add 8 to both sides of this equation to get: 

4x - 3x = 3 + 8 

combine like terms to get: 

x = 11 

x is the denominator. 

the numerator is equal to x-3 = 8 

original fraction is 8/11 

add 1 to both numerator and denominator and you get 9/12 

9/12 is the same as 3/4 confirming the value for x = 11 is good. 

answer to your question is: 

your original fraction is 8/11 .

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