Question

SOLVE FOR x =1/x+2 +1/x =3/4

Answer 1

Answer:

$\frac{1}{x + 2} + \frac{1}{x} = \frac{3}{4} \\ \\ \\ \\ \\ = > \frac{x + x + 2}{x(x + 2)} = \frac{3}{4} \\ \\ = > \frac{2x + 2}{x(x + 2)} = \frac{3}{4 } \\ \\ = > 4(2x + 2) = 3x(x + 2) \\ \\ = > 8x + 8 = 3 {x}^{2} + 6x \\ \\ \\ = > 2x + 8 = 3 {x}^{2} \\ \\ \\ = > 3 {x}^{2} - 2x - 8 = 0 \\ \\ = > 3{x}^{2} - 6x + 4x - 8 = 0 \\ \\ = > 3x(x - 2) + 4(x - 2) \\ \\ = > (3x + 4)(x - 2) = 0 \\ \\ \\ = > x = 2 \\ \\ \\ = > 3x + 4 = 0 \\ \\ x = \frac{ - 4}{3}$

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