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    If 1x+23=12x+34 \frac{1}{x} + \frac{2}{3} = \frac{1}{2x} + \frac{3}{4} x1​+32​=2x1​+43​​ then the value of x is:
    Question

    If 1x+23=12x+34 \frac{1}{x} + \frac{2}{3} = \frac{1}{2x} + \frac{3}{4} ​ then the value of x is:

    A.

    2

    B.

    8

    C.

    6

    D.

    4

    Correct option is C

    Given equation: 1x+23=12x+34Multiply both sides by the common denominator 12x:12x(1x+23)=12x(12x+34)12+8x=6+9x8x9x=612x=6x=6\text{Given equation: } \frac{1}{x} + \frac{2}{3} = \frac{1}{2x} + \frac{3}{4} \\\text{Multiply both sides by the common denominator } 12x: \\12x \left( \frac{1}{x} + \frac{2}{3} \right) = 12x \left( \frac{1}{2x} + \frac{3}{4} \right) \\12 + 8x = 6 + 9x \\8x - 9x = 6 - 12 \\-x = -6 \\x = 6​​

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