Question

Resolver la sg. ecuación:
help please
$\frac{3}{ x} - \frac{5}{x + 2} = 2$
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Answer 1

Explicación paso a paso:

$\frac{3}{ x} - \frac{5}{x + 2} = 2$

$\frac{3}{ x} = 2 + \frac{5}{x + 2}$

$\frac{3}{ x} = \frac{2x + 9}{x + 2}$

$3(x + 2) = x(2x + 9)$

$3x + 6 = 2x^{2} + 9x$

$2x^{2} + 9x = 3x + 6$

$2x^{2} + 6x - 6 = 0$

$x^{2} + 3x - 3 = 0$

$x=\frac{-b \: \pm \: \sqrt{b^{2}-4ac} }{2a}$

$x=\frac{-3 \: \pm \: \sqrt{3^{2}-4(1)( - 3)} }{2(1)}$

$x_{1,2} =\frac{-3 \: \pm \: \sqrt{21} }{2}$

$x_{1} =\frac{-3 + \sqrt{21} }{2} = 0.7913$

$x_{2} =\frac{-3 - \sqrt{21} }{2} = - 3.7913$

Por tanto:

$x = \[\left \{\begin{array}{r} 0.7913 \\ - 3.7913 \end{array}\right .\]$

Answer 2

Explicación paso a paso:

Resolvemos:

3/x - 5/(x + 2) = 2                                      //El MCM es x(x+2)

 3(x + 2) - 5x = 2x(x + 2)

   3x + 6 - 5x = 2x² + 4x

           6 - 2x = 2x² + 4x

                  0 = 2x² + 4x + 2x - 6

                  0 = 2x² + 6x - 6

                  0 = x² + 3x - 3

                  0 = x² + 2(x)(3/2) + (3/2)² - (3/2)² - 3

                  0 = (x + 3/2)² - 9/4 - 3

         9/4 + 3 = (x + 3/2)²

     (9 + 12)/4 = (x + 3/2)²

             13/4 = (x + 3/2)²

     (x + 3/2)² = 13/4

   x + 3/2 = √(13/4)           y          x + 3/2 = -√(13/4)

   x + 3/2 =  √13/2                        x + 3/2 = -√13/2

            x = -3/2 + √13/2                        x = -3/2 -√13/2

Respuesta: El C.S. = {-3/2 - √13/2 , -3/2 + √13/2}

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