Question

Calculati: a.(1 supra 21 + 1 supra 14) - (1 supra 35 - 1 supra 42) - (1 supra 14 - 1 supra 21)

Answer 1

$\bigg(\dfrac{1}{21} + \dfrac{1}{14} \bigg) - \bigg(\dfrac{1}{35} - \dfrac{1}{42} \bigg) - \bigg(\dfrac{1}{14} - \dfrac{1}{21} \bigg) =$

desfacem parantezele și respectăm regula semnelor:

$\boxed{+(+)=+} \ \boxed{-(-)=+} \ \boxed{+(-)=-} \ \boxed{-(+)=-}$

$= \dfrac{1}{21} + \dfrac{1}{14} - \dfrac{1}{35} + \dfrac{1}{42} - \dfrac{1}{14} + \dfrac{1}{21}$

reducem termenii asemenea:

$= \dfrac{1}{21} - \dfrac{1}{35} + \dfrac{1}{42} + \dfrac{1}{21}$

aducem la același numitor:

21=3×7;  35=5×7;  42=2×3×7

c.m.m.m.c. [21;35;42] = 2×3×5×7 = 210

210:21=10;  210:35=6;  210:42=5

$= \dfrac{^{10)} 1}{21} - \dfrac{^{6)}1}{35} + \dfrac{^{5)}1}{42} + \dfrac{^{10)}1}{21}$

$= \dfrac{10-6+5+10}{210} = \bf \dfrac{19}{210}$