Question

HELP ASAP pleaseeeCourse Activity Relationships Between Real NumbersPart DNow examine the sum of a rational number, y, and an irrational number, x. The rational number y can be written as ywhere a and b are integers and b *0. Leave the Irrational number xas x because it can't be written as the ratio of twointegers.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 insteadof an irrational number. Let the sum equal m, where mand n are integers and n* O. The process for rewriting the sum forx is shownReasonStatementsubstitutionx +subtraction property of equality=) 2) - ()Create common denominatorsSimplifyBased on what we established about the classification of x and using the closure of integers, what does the equation tellyou about the type of number x must be for the sum to be rational? What conclusion can you now make about the resultof adding a rational and an irrational number?BIU*, Font Sizes1

Answer 1

(bm/bn) - (an/bn) = (bm - an)/(bn)

That is a rational because it is the quotient or fraction of two integers:

_ (bm - an) is an integer

_ (bn) is an integer

(bm - an)/(bn) = x

Therefore, the left part of the equality is rational. And that part on the left must be equal to the part on the right, which is x (irrational).

This means that if the sum is rational it implies that x is rational

which goes against the initial assumption that x is irrational.