Question

simplifiquei a expressão
3(-1/2)^2+1/4
3(-1/3)^2-3/2
obtemos número:
a)-6/7
b)-7/6
c)6/7
d)7/6
e)-5/7
por favor me ajudem nesta questão,se possível,explicar passo a passo de como resolveu ficaria grato.
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Answer 1

Resposta:

A alternativa correta é a letra a.

Explicação passo-a-passo:

$\dfrac{3\;.\;\left(-\dfrac{1}{2}\right)^2+\dfrac{1}{4}}{3\;.\;\left(-\dfrac{1}{3}\right)^2-\dfrac{3}{2}}\\\\\\\dfrac{3\;.\;\left(-\dfrac{1}{2}\;.\;-\dfrac{1}{2}\right)+\dfrac{1}{4}}{3\;.\;\left(-\dfrac{1}{3}\;.\;-\dfrac{1}{3}\right)-\dfrac{3}{2}}\\\\\\\dfrac{3\;.\;\dfrac{1}{4}+\dfrac{1}{4}}{3\;.\;\dfrac{1}{9}-\dfrac{3}{2}}\\\\\\\dfrac{\dfrac{3}{4}+\dfrac{1}{4}}{\dfrac{3}{9}-\dfrac{3}{2}}\\\\\\\dfrac{\dfrac{4}{4}}{\dfrac{1}{3}-\dfrac{3}{2}}\\\\\\\dfrac{1}{\dfrac{1}{3}-\dfrac{3}{2}}$

O m.m.c de 3 e 2 é igual a 6. Logo,

$\dfrac{1}{\dfrac{2\;.\;1-3\;.\;3}{6}}\\\\\\\dfrac{1}{\dfrac{2-9}{6}}\\\\\\\dfrac{1}{\dfrac{-7}{6}}\\\\\\1\;.\;\dfrac{-6}{7}\\\\\\\boxed{-\dfrac{6}{7}} \quad \rightarrow \quad \mathbf{letra\;a}$