Question

Помогите плиз.знаменатель обыкновенной дроби больше ее числителя на 3.если к числителю этой дроби прибавить 7,а к знаменателю 5 то она увеличится на 0,5.найдите эту дробь

Answer 1

X - 1 Числитель = (x+7
(x + 3) - 2 Знаменатель = (x+8)
x+7/x+8 - x/x+3 = 1/2
x²+7x-18=0
x,=2
x,= --9 (не является)
х =2  х/х+3 = 2/5
Ответ:2/5

Answer 2

Problem Analysis

We are given a fraction where the denominator is 3 more than the numerator. If we add 7 to the numerator and 5 to the denominator, the fraction increases by 0.5. We need to find this fraction.

Solution

Let's assume the numerator of the fraction is x. According to the given information, the denominator is x + 3.

If we add 7 to the numerator, it becomes x + 7. If we add 5 to the denominator, it becomes x + 3 + 5 = x + 8.

According to the problem, the fraction increases by 0.5 when we add 7 to the numerator and 5 to the denominator. Mathematically, we can represent this as:

((x + 7) / (x + 8)) - (x / (x + 3)) = 0.5

To solve this equation, we can simplify it by multiplying both sides by the common denominator, which is (x + 8)(x + 3):

(x + 7)(x + 3) - x(x + 8) = 0.5(x + 8)(x + 3)

Expanding and simplifying the equation:

x^2 + 10x + 21 - x^2 - 8x = 0.5x^2 + 6x + 12

2x^2 + 12x + 21 - 8x - 12 = 0.5x^2 + 6x + 12

1.5x^2 - 2x - 9 = 0

Now, we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1.5, b = -2, and c = -9:

x = (-(-2) ± √((-2)^2 - 4 * 1.5 * (-9))) / (2 * 1.5)

Simplifying further:

x = (2 ± √(4 + 54)) / 3

x = (2 ± √58) / 3

Therefore, the two possible values for x are:

x = (2 + √58) / 3 and x = (2 - √58) / 3

Since the denominator of the fraction is x + 3, we can substitute the values of x to find the two possible fractions:

1. Fraction 1: ((2 + √58) / 3) / ((2 + √58) / 3 + 3) 2. Fraction 2: ((2 - √58) / 3) / ((2 - √58) / 3 + 3)

Simplifying these fractions will give us the final answers.

Please note that the values of x obtained from the quadratic equation are approximate values.