Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c. (a) a = 12, b = – 4, c = 2 (b) a = (–10), b = 1, c = 1
Solution and Explanation
(a) Given: a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)
a = 12, b = -4, c = 2
Putting the given values in L.H.S. = 12 ÷ (-4 + 2) = 12 ÷ (-2) = 12 ÷ (\(-\frac{1}{2}\)) = \(-\frac{12}{2}\) = -6
Putting the given values in R.H.S. = [12 ÷ (-4)] + (12 ÷ 2) = (12 × \(-\frac{1}{4}\)) + 6 = -3 + 6 = 3
Since L.H.S. ≠ R.H.S.
Hence, verified.
(b) Given: a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)
a = - 10, b = 1, c = 1
Putting the given values in L.H.S. = -10 ÷ (1 + 1) = - 10 ÷ (2) = -5
Putting the given values in R.H.S. = [-10 ÷ 1] + (-10 ÷ 1) = -10 - 10 = -20
Since, L.H.S. ≠ R.H.S.
Hence, verified.
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