The denominator of a fraction in the simplest form is greater than the numerator by 1. If 4 is added to the numerator, and 3 is subtracted from the denominator, then the fraction itself is increased by 2 1/6 . Find the original fraction.

x/x+1= Original fraction

x+4/x-2=x/x+1+13/6
6x/6x+6+13x+13=x-4/x-2
19x+13/6x+6=x+4/x-2
(cross multiply)
6x^2+20x+24=19x^2-25x-26
55x+50=13x^2
13x^2-55x-50=0
x=5
original fraction=5/6

Anonymous's answer, 5/6 is the right answer, ignore all of the others

Answer is not right...

wrong

To solve this problem, let's let the numerator of the original fraction be represented by the variable 'x'.

According to the problem, the denominator is greater than the numerator by 1, so we can represent the denominator as 'x + 1'.

The original fraction can then be expressed as x / (x + 1).

Next, we're told that if we add 4 to the numerator and subtract 3 from the denominator, the fraction itself is increased by 2 1/6.

This tells us that the new fraction is equal to the original fraction plus 2 1/6.
In other words, (x + 4) / (x + 1 - 3) = x / (x + 1) + 2 1/6.

To simplify this equation, we need to convert the mixed number 2 1/6 into an improper fraction.

2 1/6 = (2 * 6 + 1) / 6 = 13 / 6.

So, we can rewrite the equation as:

(x + 4) / (x - 2) = x / (x + 1) + 13 / 6.

To get rid of the fractions, we multiply through by the least common multiple (LCM) of the denominators, which in this case is 6.

6 * (x + 4) = 6 * (x - 2) * x / (x + 1) + 6 * (x - 2) * 13 / 6.

Simplifying this equation, we have:

6x + 24 = 6(x - 2)(x + 1) + 13(x - 2).

Expanding the brackets, we get:

6x + 24 = 6(x^2 - x - 2) + 13x - 26.

Simplifying further,

6x + 24 = 6x^2 - 6x - 12 + 13x - 26.

Combining like terms,

6x + 24 = 6x^2 + 7x - 38.

Rearranging the equation to isolate the terms on one side,

6x^2 + 7x - 6x - 24 - 38 = 0.

Simplifying, we have,

6x^2 + x - 62 = 0.

Now, we can solve this quadratic equation for x by factoring or using the quadratic formula.

Factoring may not lead to rational solutions, so we'll use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a).

For our equation, a = 6, b = 1, and c = -62.

Plugging these values into the quadratic formula, we get:

x = (-1 ± √(1^2 - 4 * 6 * -62)) / (2 * 6).

Simplifying further,

x = (-1 ± √(1 + 1488)) / 12.

x = (-1 ± √1489) / 12.

This gives us two possible solutions for x.

If we take the positive square root:

x = (-1 + √1489) / 12.

And if we take the negative square root:

x = (-1 - √1489) / 12.

These are the solutions for the numerator of the original fraction.

To find the original fraction, we substitute each solution for x back into the original fraction expression:

Original Fraction 1: x / (x + 1) = [(-1 + √1489) / 12] / [((-1 + √1489) / 12) + 1].

Original Fraction 2: x / (x + 1) = [(-1 - √1489) / 12] / [((-1 - √1489) / 12) + 1].

Simplifying these expressions will give you the two possible original fractions.

yes that might work but not rly helpful

bro nobdy be writing answers cmon guys

current fraction = x/(x+1)

new fraction = (x+4)/(x+1 - 3)
= (x+4)/(x-2)
Their difference is 2 1/6 or 13/6
(x+4)/(x-2) - x/(x+1) = 13/6
multiply each term by 6(x+1)(x-2), the LCD
6(x+1)(x+4) - 6x(x-2) = 13(x+1)(x-2)
6x^2 + 30x + 24 - 6x^2 + 12x = 13x^2 -13x - 26
13x^2 - 55x - 50 = 0

solve using your favourite method of solving quadratics
You will get a whole number and a negative fraction.
I would just stick with the whole number answer.

Yo all!

Here is the answer to the question.

1/6

You're all welcome