rove the following statement directly from the definition of rational number. The difference of any two rational numbers is a ra
tional number. Proof: Suppose r and s are any two rational numbers. By definition of rational, r = a b and s = c d for some ---Select--- a, b, c, and d with ---Select--- . Write r − s in terms of a, b, c, and d as a quotient of two integers whose numerator and denominator are simplified as much as possible. The result is the following. r − s = Both the numerator and the denominator are integers because ---Select--- . In addition, bd ≠ 0 by the ---Select--- . Hence r − s is a ---Select--- of two integers with a nonzero denominator, and so by definition of rational, r − s is rational.
1 answer:
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Answer:
x = 3
Step-by-step explanation:
Square both sides of the equation
(x - 3)(x - 5) = 0
x = 3 or 5
Now, you must always check your results because a result may not satisfy the original equation.
If x = 3, then and 3 - x = 3 - 3 = 0
So 3 satisfies the original.
If x = 5, then , but 3 - x = 3 - 5 = -2. Therefore, 5 does NOT satisfy the original equation.
That means that x = 3 is the solution to the equation.
