1. Fractions with unknow numbers

The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2, the fraction is increased by 1/12. Find the original fraction. (One should try to solve it by completing the square)

This is my attempt:
x+1/x+2-(x-1)/x=1/12
After that I multiplied everything with (x+2) 12x and cancelled out the numbers. I am not sure if the first equation is correct.

2. Originally Posted by Anna55
The numerator of a fraction is 1 less than the denominator. When both numerator and denominator are increased by 2, the fraction is increased by 1/12. Find the original fraction. (One should try to solve it by completing the square)

This is my attempt:
x+1/x+2-(x-1)/x=1/12
After that I multiplied everything with (x+2) 12x and cancelled out the numbers. I am not sure if the first equation is correct.

$\dfrac{x+1}{x+2} - \dfrac{x-1}{x} = \dfrac{1}{12}$

... and your subsequent method will work fine.

3. I tried to solve the equation, however I got the wrong answer. Can you please show me how to solve it? Thank you!

4. When you expand and simplify $12x(x+1)-12(x+2)(x-1)=x(x+2)$
what did you get?

5. I got this:
(x+1)12x-(x-1)12(x+2)=1x (x+2)
12x^2+12x-(x-1)12x+24=x^2+2x
Did I make a mistake?

6. Originally Posted by Anna55
I got this:
(x+1)12x-(x-1)12(x+2)=1x (x+2)
12x^2+12x-(x-1)12x+24=x^2+2x
Did I make a mistake?
The part in red should be $-12x^2-12x+24$

7. You haven't multiplied the -(x-1) by 24 as well as the 12x. The 12x+24 should be in brackets i.e -(x-1)(12x+24)...

8. You should end up with x^2 +12x-24=0

9. Originally Posted by orlacoon
You should end up with x^2 +12x-24=0
incorrect ... $x^2 + 2x - 24 = 0$

10. Sorry-Typo

Sorry- that was a typo. Meant to say x^2+2x-24=0. The equation x^2+12x-24=0 is what you would get using the asker's workings out!