Explicación paso a paso:
(3x-2)(x+1)=2
3x² + 3x - 2x -2 =2
3x² + x -2 -2=0
3x² + x -4=0
Donde:
a = 3
b = 1
c = -4
Desarrollamos:
[tex]x_{1,\:2}=\frac{-\left(1\right)\pm \sqrt{\left(1\right)^2-4\cdot \:3\cdot \:-4}}{2\cdot \:3} \\\\ x_{1,\:2}=\frac{-1\pm \sqrt{1+48}}{6} \\\\ x_{1,\:2}=\frac{-1\pm \sqrt{49}}{6} \\\\ x_{1,\:2}=\frac{-1\pm7}{6}[/tex]
Separar las soluciones:
[tex]x_1=\frac{-1+7}{6},\:x_2=\frac{-1-7}{6} \\\\ x_1=\frac{6}{6},\:x_2=\frac{-8}{6} \\\\ x_1=1,\:x_2=\frac{-4}{3}[/tex]
(2x)/(x-1)+(4)/(x+2)=5
2x(x+2) + 4(x-1) = 5(x+2) (x-1)
2x² + 4x + 4x - 4 = 5(x²-x+2x-2)
2x² + 8x - 4 = 5(x²+x-2)
2x² + 8x - 4 = 5x² +5x - 10
2x²-5x² + 8x -5x - 4 +10 = 0
-3x² + 3x + 6 = 0
Donde:
a = -3
b = 3
c = 6
Desarrollamos:
[tex]x_{1,\:2}=\frac{-\left(3\right)\pm \sqrt{\left(3\right)^2-4\cdot \:-3\cdot \:6}}{2\cdot \:-3} \\\\ x_{1,\:2}=\frac{-3\pm \sqrt{9+72}}{-6} \\\\ x_{1,\:2}=\frac{-3\pm \sqrt{81}}{-6} \\\\ x_{1,\:2}=\frac{-3\pm9}{-6}[/tex]
Separar las soluciones:
[tex]x_1=\frac{-3+9}{-6},\:x_2=\frac{-3-9}{-6} \\\\ x_1=\frac{6}{-6},\:x_2=\frac{-12}{-6} \\\\ x_1=-1,\:x_2=2[/tex]
