Why do some, insignificant parentheses change the answer?

Question

C++ / C#

I wrote a program that was supposed to calculate the recurrent formula.
I didn't get the answers. I decided to remove some brackets and everything came together.
Can you please explain how formula 1 differs from formula 2?
Why is there one answer for the first formula and another for the second?
Maybe the problem was in the priority of operations?

1)a = a * (-x)*(2*i+1)/(2*i);
2)a = a * (-x)*((2*i+1)/(2*i));

The value according to the control formula should be equal to the sum, taking into account the error.
C++ language:

#include <iostream>
#include <stdio.h>
#include <math.h>

using namespace std;

int main()
{
    double s,x,e,a,y;
    int i = 1;
    cout<<"Аргумент: "<<endl;
    cin>>x;
    cout<<"Погрешность: "<<endl;
    cin>>e;

    a = 1;
    s = a;
    y= 1/sqrt(pow((1+x),3));

    while(e <= abs(a))
    {
        a = a *(-1*x)*((2*i+1)/(2*i));
        s +=a;
        i++;
    }

    cout<<"Сумма ряда"<<endl;
    cout<<s<<endl;
    cout<<"Контрольная формула "<<endl;
    cout<<y;

    return 0;
}

Answer 1

(-x)*(2*i+1)/(2*i)- a real number is multiplied by an integer, the result is real, then a real number is divided by a real number, the result is real. - an integer is divided by an integer, the result is an integer , then a real number is multiplied by an integer, the result is real.
(-x)*((2*i+1)/(2*i))