Question

Если к числителю некоторой несократимой дроби прибавить число шесть, а знаменатель этой же несократимой дроби увеличить на пятнадцать, то известно, что исходная несократимая дробь от этого не изменится. Указать эту несократимую дробь.

Answer 1

Х/у-была дробь

(х+6)/(у+15)=х/у

$\frac{x+6}{y+15} = \frac{x}{y} y(x+6)=x(y+15) yx+6y=xy+15x 6y=15x$

6y=15x
x/y=6/15
x/y=2/5

дробь была 2/5

стала 8/20=2/5

Answer 2

Problem Analysis

We are given an equation involving an irreducible fraction. The numerator of the fraction is increased by 6, while the denominator is increased by 15. We need to find the original irreducible fraction.

Solution

Let's assume the original irreducible fraction is x/y. According to the given information, we have the following equation:

(x + 6) / (y + 15) = x / y

To solve this equation, we can cross-multiply:

y(x + 6) = x(y + 15)

Expanding both sides of the equation:

xy + 6y = xy + 15x

Simplifying the equation:

6y = 15x

Dividing both sides of the equation by 3:

2y = 5x

Since we are looking for an irreducible fraction, the numerator and denominator must be coprime (they have no common factors other than 1). Therefore, we can conclude that y = 5 and x = 2.

Hence, the original irreducible fraction is 2/5.

Answer

The original irreducible fraction, when the numerator is increased by 6 and the denominator is increased by 15, remains unchanged and is equal to 2/5.