Question

1/(x+2)+1/x=3/4 find x

Answer 1

Answer:

The solution is below.

Step-by-step explanation:

$\frac{1}{x + 2} + \frac{1}{x} = \frac{3}{4}$

$= > \frac{x + (x + 2)}{x(x + 2)} = \frac{3}{4}$

$= > \frac{2x + 2}{ {x}^{2} + 2x} = \frac{3}{4}$

$= > 8x + 8 = 3 {x}^{2} + 6x$

$= > 3 {x}^{2} - 2x - 8 = 0$

$= > 3{x}^{2} - (6 - 4)x - 8x$

$= > 3{x}^{2} - 6x + 4x - 8 = 0$

$= > 3x(x - 2) + 4(x - 2) = 0$

$= > (x - 2)(3x + 4) = 0$

So , x will have the values : 2 or -4/3

Hope this helps you.

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