The denominator of a fraction is 2 less than twice the numberator. If the numerator is decreased by 2 and the denominator is increased by 3, the resulting fraction simplifies to 1/3. Find the original fraction.

Have no idea what to do.

To solve this problem, let's assume the original fraction is represented by the numerator (N) and the denominator (D).

According to the problem, the denominator (D) is 2 less than twice the numerator (N). So we can write the equation:

D = 2N - 2

It is also given that if we decrease the numerator (N) by 2 and increase the denominator (D) by 3, the resulting fraction simplifies to 1/3. This can be represented as:

(N - 2) / (D + 3) = 1/3

To find the original fraction, we need to solve these two equations simultaneously. Let's substitute the value of D from the first equation into the second equation:

(N - 2) / (2N - 2 + 3) = 1/3

(N - 2) / (2N + 1) = 1/3

Now, cross-multiply the equation:

3(N - 2) = 1(2N + 1)

3N - 6 = 2N + 1

Combine like terms:

3N - 2N = 1 + 6

N = 7

Substituting N = 7 into the first equation to find D:

D = 2(7) - 2

D = 12

Therefore, the original fraction is 7/12.

To find the original fraction, we can start by setting up equations based on the given information.

Let's say the numerator of the fraction is represented by the variable 'x' and the denominator is represented by the variable 'y'.

According to the problem, we have two pieces of information:
1) The denominator is 2 less than twice the numerator, which can be written as: y = 2x - 2.
2) When the numerator is decreased by 2 (x - 2) and the denominator is increased by 3 (y + 3), the resulting fraction simplifies to 1/3.

To solve the problem, we need to express the original fraction in terms of 'x' and 'y', and then use the second piece of information to find the values of 'x' and 'y'.

We can use the formula for fraction simplification: (numerator - n) / (denominator + n), where 'n' represents the amount by which both the numerator and denominator are changed.

Using this formula, we get the equation: (x - 2) / (y + 3) = 1/3.

Now, we have a system of two equations:
1) y = 2x - 2
2) (x - 2) / (y + 3) = 1/3

To solve this system of equations, we can substitute the value of 'y' given by the first equation into the second equation and solve for 'x'.

Substituting y = 2x - 2 into the second equation, we get: (x - 2) / ((2x - 2) + 3) = 1/3.

Simplifying this expression, we get: (x - 2) / (2x + 1) = 1/3.

Now, cross-multiplying the equation, we have: 3(x - 2) = (2x + 1).

Expanding and solving for 'x', we get: 3x - 6 = 2x + 1.

Bringing the variables to one side and the constants to the other side, we have: 3x - 2x = 1 + 6.

Simplifying this further, we get: x = 7.

Now that we have found the value of 'x', we can substitute it into the first equation to find the value of 'y'.

Using y = 2x - 2, we get: y = 2 * 7 - 2 = 12.

Therefore, the original fraction is 7/12.

n/d = n/(2n-1)

(n-2)/(2n+2) = 1/3
3n - 6 = 2n + 2

n = 8
d = 15
so
n/d = 8/15