1/(x+2)+1/x=3/4 find x
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Answer:
The solution is below.
Step-by-step explanation:
[tex] \frac{1}{x + 2} + \frac{1}{x} = \frac{3}{4} [/tex]
[tex] = > \frac{x + (x + 2)}{x(x + 2)} = \frac{3}{4} [/tex]
[tex] = > \frac{2x + 2}{ {x}^{2} + 2x} = \frac{3}{4} [/tex]
[tex] = > 8x + 8 = 3 {x}^{2} + 6x[/tex]
[tex] = > 3 {x}^{2} - 2x - 8 = 0[/tex]
[tex] = > 3{x}^{2} - (6 - 4)x - 8x[/tex]
[tex] = > 3{x}^{2} - 6x + 4x - 8 = 0[/tex]
[tex] = > 3x(x - 2) + 4(x - 2) = 0[/tex]
[tex] = > (x - 2)(3x + 4) = 0[/tex]
So , x will have the values : 2 or -4/3
Hope this helps you.
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