The denominator of a fraction is 2 more than the numerator.If 1 is subtracted from both numerator and denominator,the result in fraction has value of 1/2.Find the original faction.
the original fraction is
x/(x+2)
(x-1)/(x+2-1) = 1/2
now just solve for x.
Let's proceed step-by-step to find the original fraction.
Step 1: Let's assume the numerator of the original fraction as "x".
Step 2: According to the problem, the denominator of the fraction is 2 more than the numerator. Therefore, the denominator would be (x + 2).
Step 3: If 1 is subtracted from both numerator and denominator, the resulting fraction is 1/2. So, we have:
(x - 1)/(x + 2 - 1) = 1/2
Simplifying this equation, we get:
(x - 1)/(x + 1) = 1/2
Step 4: To get rid of the fraction, we can cross multiply:
2(x - 1) = (x + 1)
Step 5: Expanding the equation:
2x - 2 = x + 1
Step 6: Simplifying the equation by combining like terms:
2x - x = 1 + 2
x = 3
Step 7: Now that we have found the value of x, which is 3, we can substitute it back into the original fraction. The numerator would be 3, and the denominator would be (3 + 2) = 5.
Therefore, the original fraction is 3/5.
To solve this problem, let's break it down step by step:
Step 1: Let's represent the numerator of the fraction as x.
Step 2: Since the denominator is 2 more than the numerator, we can represent it as (x + 2).
Step 3: If 1 is subtracted from both the numerator and denominator, the resulting fraction can be expressed as (x - 1)/(x + 2 - 1) = (x - 1)/(x + 1).
Step 4: According to the problem, the resulting fraction is equal to 1/2, so we have:
(x - 1)/(x + 1) = 1/2.
Now, let's solve this equation:
Step 5: To eliminate fractions, we can multiply both sides of the equation by the least common denominator, which in this case is 2(x + 1):
2(x - 1) = (x + 1) * 1.
Step 6: Simplify the equation:
2x - 2 = x + 1.
Step 7: Move all the terms involving x to one side of the equation and the constant terms to the other side:
2x - x = 1 + 2.
Step 8: Simplify:
x = 3.
Step 9: Now that we have found the value of x, we can substitute it back into the original expression to find the fraction:
Fraction = x / (x + 2) = 3 / (3 + 2) = 3/5.
Therefore, the original fraction is 3/5.