Question

Знаменатель обыкновенной дроби на 4Знаменатель обыкновенной дроби на 4 меньше числителя.Если знаменатель уменьшить на 1,а числитель на 4, то дробь уменьшится на 5/6. найдите эту дробь. Помогите пожалуйста!!!

Answer 1

Знаменатель х , числитель х+4. Уравнение: (Х+4)/х- (х+4-4)/(х-1)=5/6 6(х+4)(х-1)-6х^2=5х(х-1) 18х-24=5х^2-5х 5х^2-23х+24=0 Д=529-480=49 Х1=3, х2=1,6. Тогда числители будут 7 и 5,6. Дроби получаются 7/3 и 5,6/1,6=7/2

Answer 2

(х+4) / х -- это "Знаменатель обыкновенной дроби на 4 меньше числителя"))) 
((х+4) / х) - (х / (х-1)) = 5/6 
6(х+4)*(х-1) - 6х² = 5х(х-1) 
18х - 24 = 5х² - 5х 
5х² - 23х + 24 = 0
D = 23*23 - 4*5*24 = 529-480 = 7²
x1 = (23 - 7) / 10 = 1.6 --не может быть знаменателем обыкновенной дроби)))
x2 = 3
Эта дробь: 7/3
ПРОВЕРКА: (7-4)/(3-1) = 3/2
3/2 + 5/6 = 14/6 = 7/3

Answer 3

Finding the Fraction

To find the fraction described in the problem, we need to solve the given equation. Let's break down the problem step by step:

1. Let the denominator of the fraction be x. 2. According to the problem, if we decrease the denominator by 1 and the numerator by 4, the fraction decreases by 5/6. 3. Mathematically, we can represent this as:

(x - 1)/(x) = (x - 4)/(x) - 5/6

Now, let's solve this equation to find the value of x.

Solving the Equation

To solve the equation, we can cross-multiply and simplify:

(x - 1)/(x) = (x - 4)/(x) - 5/6

Cross-multiplying:

6(x - 1) = 6(x - 4) - 5x

Expanding:

6x - 6 = 6x - 24 - 5x

Simplifying:

6x - 6 = x - 24

Moving all the terms to one side:

6x - x = -24 + 6

Simplifying:

5x = -18

Dividing both sides by 5:

x = -18/5

Therefore, the denominator of the fraction is -18/5.

The Fraction

Now that we have found the value of the denominator, we can substitute it back into the original equation to find the fraction.

Substituting x = -18/5 into the equation:

(-18/5 - 1)/(-18/5) = (-18/5 - 4)/(-18/5) - 5/6

Simplifying:

(-23/5)/(-18/5) = (-38/5)/(-18/5) - 5/6

Simplifying further:

(-23/5) * (-5/18) = (-38/5) * (-5/18) - 5/6

Cancelling out common factors:

23/18 = 38/18 - 5/6

Simplifying:

23/18 = 38/18 - 15/18

Combining the fractions:

23/18 = 23/18

Therefore, the fraction is 23/18.

I hope this helps! Let me know if you have any further questions.