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Begin by simplifying the left fraction: a a + b = 1 + a b = 1 + x 1 .
Therefore, 1 + x 1 = x .
Multiply by x: x + 1 = x 2
Rearrange: x 2 − x − 1 = 0
Use the quadratic formula: x = 2 1 + 5
(note: Remember that, at the beginning, x is a positive ratio, so, you add).