SOLUTION: the denominator of a fraction exceeds the numerator by 2. If the numerator is decreased by 1 and the denominator is increased by 3,the value of the resulting fraction is 1/2 find t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: the denominator of a fraction exceeds the numerator by 2. If the numerator is decreased by 1 and the denominator is increased by 3,the value of the resulting fraction is 1/2 find t      Log On


   

Question 1063043: the denominator of a fraction exceeds the numerator by 2. If the numerator is decreased by 1 and the denominator is increased by 3,the value of the resulting fraction is 1/2 find the original fraction? with linear equation
Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Original fraction,
X%2F%28X%2B2%29
New fraction,
%28X-1%29%2F%28X%2B2%2B3%29=%28X-1%29%2F%28X%2B5%29
So then,
%28X-1%29%2F%28X%2B5%29=%281%2F2%29%28X%2F%28X%2B2%29%29
2%28X-1%29%28X%2B2%29=X%28X%2B5%29
2%28X%5E2%2B2X-X-2%29=X%5E2%2B5X
2X%5E2%2B2X-4=X%5E2%2B5X
X%5E2-3X-4=0
%28X-4%29%28X%2B1%29=0
Two solutions:
X-4=0
X=4
and
X%2B1=0
X=-1
So the original fraction was
4%2F%284%2B2%29=4%2F6=2%2F3
or
-1%2F%28-1%2B2%29=-1%2F1=-1

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

the denominator of a fraction exceeds the numerator by 2. If the numerator is decreased by 1 and the denominator is increased by 3,the value of the resulting fraction is 1/2 find the original fraction? with linear equation
Original fraction: highlight_green%287%2F9%29