Answer:
The value of x is 2.
Step-by-step explanation:
First, you have to make the left side into 1 fraction by making the denorminator the same :
[tex] \frac{x}{x - 2} + \frac{1}{5} [/tex]
[tex] = \frac{5x}{5(x - 2)} + \frac{x - 2}{5(x - 2)} [/tex]
[tex] = \frac{5x + x - 2}{5(x - 2)} [/tex]
[tex] = \frac{6x - 2}{5(x - 2)} [/tex]
Then you have to do cross multiplication :
[tex] \frac{6x - 2}{5(x - 2)} = \frac{2}{x - 2} [/tex]
[tex](6x - 2)(x - 2) = 5(2)(x - 2)[/tex]
[tex]6 {x}^{2} - 12x - 2x + 4 = 10x - 20[/tex]
[tex]6 {x}^{2} - 14x + 4 = 10x - 20[/tex]
[tex]6 {x}^{2} - 14x + 4 - 10x + 20 = 0[/tex]
[tex]6 {x}^{2} - 24x + 24 = 0[/tex]
[tex]6( {x}^{2} - 4x + 4) = 0[/tex]
[tex]{x}^{2} - 4x + 4 = 0[/tex]
[tex]{x}^{2} - 2x - 2x + 4 = 0[/tex]
[tex]x(x - 2) - 2(x - 2) = 0[/tex]
[tex](x - 2)(x - 2) = 0[/tex]
[tex]x = 2[/tex]
