Question

PLEASE HELP ASAP AND THANKS Find x

Answer 1

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 :

$\frac{x}{x - 2} + \frac{1}{5}$

$= \frac{5x}{5(x - 2)} + \frac{x - 2}{5(x - 2)}$

$= \frac{5x + x - 2}{5(x - 2)}$

$= \frac{6x - 2}{5(x - 2)}$

Then you have to do cross multiplication :

$\frac{6x - 2}{5(x - 2)} = \frac{2}{x - 2}$

$(6x - 2)(x - 2) = 5(2)(x - 2)$

$6 {x}^{2} - 12x - 2x + 4 = 10x - 20$

$6 {x}^{2} - 14x + 4 = 10x - 20$

$6 {x}^{2} - 14x + 4 - 10x + 20 = 0$

$6 {x}^{2} - 24x + 24 = 0$

$6( {x}^{2} - 4x + 4) = 0$

${x}^{2} - 4x + 4 = 0$

${x}^{2} - 2x - 2x + 4 = 0$

$x(x - 2) - 2(x - 2) = 0$

$(x - 2)(x - 2) = 0$

$x = 2$