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Boa noite Luiz!
Solução!
![\dfrac{x-2}{3x}+ \dfrac{2x-1}{2} = \dfrac{5x+2}{6}\\\\\\
MMC=36x\\\\\\
12(x-2)+18x(2x-1)=6x(5x+2)\\\\\\
12x-24+36 x^{2} -18x=30 x^{2} +12x\\\\\\\
36 x^{2} -30 x^{2} +12x-12x-18x-24=0\\\\\\\
6 x^{2} -18x-24=0\\\\\\\
Vamos~~dividir~~a~~equac\~ao~~por~~6!](https://tex.z-dn.net/?f=+%5Cdfrac%7Bx-2%7D%7B3x%7D%2B+%5Cdfrac%7B2x-1%7D%7B2%7D+%3D+%5Cdfrac%7B5x%2B2%7D%7B6%7D%5C%5C%5C%5C%5C%5C%0A%0AMMC%3D36x%5C%5C%5C%5C%5C%5C%0A12%28x-2%29%2B18x%282x-1%29%3D6x%285x%2B2%29%5C%5C%5C%5C%5C%5C%0A12x-24%2B36+x%5E%7B2%7D+-18x%3D30+x%5E%7B2%7D+%2B12x%5C%5C%5C%5C%5C%5C%5C%0A36+x%5E%7B2%7D+-30+x%5E%7B2%7D+%2B12x-12x-18x-24%3D0%5C%5C%5C%5C%5C%5C%5C%0A6+x%5E%7B2%7D+-18x-24%3D0%5C%5C%5C%5C%5C%5C%5C%0AVamos%7E%7Edividir%7E%7Ea%7E%7Eequac%5C%7Eao%7E%7Epor%7E%7E6%21 "\dfrac{x-2}{3x}+ \dfrac{2x-1}{2} = \dfrac{5x+2}{6}\\\\\\
MMC=36x\\\\\\
12(x-2)+18x(2x-1)=6x(5x+2)\\\\\\
12x-24+36 x^{2} -18x=30 x^{2} +12x\\\\\\\
36 x^{2} -30 x^{2} +12x-12x-18x-24=0\\\\\\\
6 x^{2} -18x-24=0\\\\\\\
Vamos~~dividir~~a~~equac\~ao~~por~~6!")
![6 x^{2} -18x-24=0:6\\\\\\\
x^{2} -3x-4=0\\\\\
Vamos ~~usar~~ a ~~formula ~~de~~ Bhaskara!](https://tex.z-dn.net/?f=6+x%5E%7B2%7D+-18x-24%3D0%3A6%5C%5C%5C%5C%5C%5C%5C%0A+x%5E%7B2%7D+-3x-4%3D0%5C%5C%5C%5C%5C%0AVamos+%7E%7Eusar%7E%7E+a+%7E%7Eformula+%7E%7Ede%7E%7E+Bhaskara%21 "6 x^{2} -18x-24=0:6\\\\\\\
x^{2} -3x-4=0\\\\\
Vamos ~~usar~~ a ~~formula ~~de~~ Bhaskara!")
![a=1~~~~~b=-3~~~~~~c=-4\\\\\\\
x= \dfrac{-b\pm \sqrt{b^{2}-4.a.c } }{2.a}\\\\\\
x= \dfrac{-(-3)\pm \sqrt{(-3)^{2}-4.1.(-4) } }{2.1}\\\\\\
x= \dfrac{3\pm \sqrt{9+16 } }{2}\\\\\\
x= \dfrac{3\pm \sqrt{25 } }{2}\\\\\\
x= \dfrac{3\pm 5}{2}\\\\\\\\
x_{1}= \dfrac{3+5}{2}= \dfrac{8}{2}=4\\\\\\
x_{2}= \dfrac{3-5}{2}= \dfrac{-2}{2}=-1\\\\\\\\\
\boxed{Resposta:S=\{-1,4\}~~\boxed{Alternativa~~B}}](https://tex.z-dn.net/?f=a%3D1%7E%7E%7E%7E%7Eb%3D-3%7E%7E%7E%7E%7E%7Ec%3D-4%5C%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B-b%5Cpm+%5Csqrt%7Bb%5E%7B2%7D-4.a.c+%7D+%7D%7B2.a%7D%5C%5C%5C%5C%5C%5C%0A%0Ax%3D+%5Cdfrac%7B-%28-3%29%5Cpm+%5Csqrt%7B%28-3%29%5E%7B2%7D-4.1.%28-4%29+%7D+%7D%7B2.1%7D%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B3%5Cpm+%5Csqrt%7B9%2B16+%7D+%7D%7B2%7D%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B3%5Cpm+%5Csqrt%7B25+%7D+%7D%7B2%7D%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B3%5Cpm+5%7D%7B2%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A+x_%7B1%7D%3D+%5Cdfrac%7B3%2B5%7D%7B2%7D%3D+%5Cdfrac%7B8%7D%7B2%7D%3D4%5C%5C%5C%5C%5C%5C%0Ax_%7B2%7D%3D+%5Cdfrac%7B3-5%7D%7B2%7D%3D+%5Cdfrac%7B-2%7D%7B2%7D%3D-1%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3AS%3D%5C%7B-1%2C4%5C%7D%7E%7E%5Cboxed%7BAlternativa%7E%7EB%7D%7D%0A%0A "a=1~~~~~b=-3~~~~~~c=-4\\\\\\\
x= \dfrac{-b\pm \sqrt{b^{2}-4.a.c } }{2.a}\\\\\\
x= \dfrac{-(-3)\pm \sqrt{(-3)^{2}-4.1.(-4) } }{2.1}\\\\\\
x= \dfrac{3\pm \sqrt{9+16 } }{2}\\\\\\
x= \dfrac{3\pm \sqrt{25 } }{2}\\\\\\
x= \dfrac{3\pm 5}{2}\\\\\\\\
x_{1}= \dfrac{3+5}{2}= \dfrac{8}{2}=4\\\\\\
x_{2}= \dfrac{3-5}{2}= \dfrac{-2}{2}=-1\\\\\\\\\
\boxed{Resposta:S=\{-1,4\}~~\boxed{Alternativa~~B}}")
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Bons estudos!
Solução!
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Bons estudos!
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