x + 2 = 15/x

1/x - 2/x-3 = 4

Now multiply by x on both sides, we get

x^2 + 2x = 15

x^2 + 2x - 15 = 0

x^2 - 3x + 5x - 15 = 0

x(x - 3) + 5(x - 3) = 0

(x - 3)(x + 5) = 0

x = 3 x = - 5

x = {3, -5}

Now multiply by x(x - 3) on both side, we get

1(x - 3) - 2x = 4x(x - 3)

x - 3 - 2x = 4x^2 - 12x

4x^2 - 12x = - 3 - x

4x^2 - 12x + x + 3 = 0

4x^2 - 11x + 3 = 0

a = 4 b = - 11 c = 3

Using quadratic formula, then

x = (- b ± √b^2 - 4ac ) / 2a

x = ( 11 ± √121 - 48 ) / 8

x = ( 11 ± √73 ) / 8

x = {( 11 + √73 ) / 8, ( 11 - √73 ) / 8}

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