Question

5. Числитель обыкновенной дроби на 3 единицы меньше знаменателя. Если к числителю и знаменателю дроби прибавить 1, то она станет равной 1/2. Найдите первоначальную дробь.​Нужно решение. 15 баллов!

Answer 1

Пошаговое объяснение:

Х знаменатель

(Х-3) числитель

(Х+1) стал знаменатель

(х-3)+1=х-2 стал числитель

(х-2)/(х+1)=1/2

Х+1=2(х-2)

Х+1=2х-4

Х-2х= - 4-1

-х= - 5

Х=5

Answer 2

Problem Analysis

We are given that the numerator of a fraction is 3 units less than the denominator. If we add 1 to both the numerator and denominator, the fraction becomes equal to 1/2. We need to find the original fraction.

Solution

Let's assume the denominator of the fraction is x. According to the problem, the numerator is 3 units less than the denominator, so it would be x - 3.

If we add 1 to both the numerator and denominator, the fraction becomes (x - 3 + 1)/(x + 1), which is equal to 1/2.

Now we can set up the equation and solve for x:

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

Simplifying the equation:

(x - 2)/(x + 1) = 1/2

Cross-multiplying:

2(x - 2) = x + 1

Expanding and simplifying:

2x - 4 = x + 1

Bringing all the x terms to one side:

2x - x = 1 + 4

x = 5

So the denominator of the original fraction is 5. And since the numerator is 3 units less than the denominator, the numerator is 5 - 3 = 2.

Therefore, the original fraction is 2/5.

Answer

The original fraction is 2/5.