Is the sum of a rational number and an irrational number an irrational number? Please certify

Is the sum of a rational number and an irrational number an irrational number? Please certify

Must be an irrational number.
Rational numbers can be reduced to two integer ratios, but irrational numbers can not.
Suppose that the sum of rational number a/b and irrational number x is rational number c/d,
Where a, b, c, d are integers and b, d are not zero
Then a/b+x=c/d, x=c/d-a/b=(bc-ad)/bd
X can be reduced to the ratio of two integers bc-ad and bd, x is a rational number,
This contradicts the assumption that x is an irrational number.
Therefore, the sum of a rational number and an irrational number can not be a rational number, it must be an irrational number.

A is rational number and x is irrational number.

The problem needs to be proved in reverse
First of all, we must understand the definition of rational numbers, rational numbers include integers and fractions, that is, as long as it is a rational number, it must be written in the form of a/b, where a and b are integers.
The following starts to prove:
CERTIFICATE:
Suppose a+x is a rational number
Let a+x=c/b (c, b are integers)
Similarly, a=e/f (e, f are integers)
Then bf (a+x) is an integer
Decomposition factor bfa+bfx
=Be + bfx
Then be+bfx is an integer
Be is obviously an integer
Then bfx is an integer
But bf is an integer, x is an irrational number, and an integer * an irrational number can not be an integer (if it can, it can be written as a/b, which is a rational number)
Therefore, be+bfx is not an integer, which contradicts the assumption
So a+x is an irrational number