the numerator of a fraction is 3 less than the denominator. if 4 us added to the numerator and to the denominator, the resulting fraction is equivalent to 3/4. find the original fraction
original fraction: (x-3)/x
(x-3+4)/(x+4) = 3/4
To find the original fraction, let's assign variables to the numerator and denominator.
Let "x" be the denominator of the fraction.
According to the given information, the numerator is 3 less than the denominator. So, the numerator can be expressed as "x - 3".
When 4 is added to both the numerator and the denominator, the resulting fraction is 3/4. To express this, we can create the equation:
(x - 3 + 4) / (x + 4) = 3/4
Now, let's solve this equation step by step:
First, simplify the equation:
(x + 1) / (x + 4) = 3/4
Next, cross multiply:
4(x + 1) = 3(x + 4)
Distribute the multiplication:
4x + 4 = 3x + 12
Subtract 3x from both sides:
4x - 3x + 4 = 12
Simplify:
x + 4 = 12
Subtract 4 from both sides:
x = 8
We have found x to be 8, which represents the denominator of the original fraction.
Now, substitute x back into the numerator expression to find the numerator:
Numerator = x - 3
= 8 - 3
= 5
Therefore, the original fraction is 5/8.