SOLUTION: The numerator of a fraction is three less than the denominator. If the numerator and denominator are each increased by 1 the value of the fraction becomes 3/4. What is the original

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Question 272665: The numerator of a fraction is three less than the denominator. If the numerator and denominator are each increased by 1 the value of the fraction becomes 3/4. What is the original fraction?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
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