Part D Now examine the sum of a rational number, y, an an irrational number, x. The
rational number y can be written as y=a/b, where a and b are integers and b≠0. Leave the irrational number x as x because it can’t be written as the ratio of two integers.
Let’s look at a proof by contradiction. In other words, we’re trying to show that x+y is equal to a rational number instead of an irrational number. Let the sum equal m/n, where m and n are integers and n≠0. The process for writing the sum for x is shown.

Based on what we established about the classification of x and using the closure of integers, what does the equation tell you about the type of number x and must be for the sum to be rational? What conclusion can you now make about the result of adding a rational and an irrational number?