I'm going to assume (x/x-18) is meant to be "x OVER x-18". (But, that's not how it's written.) Same way with (11/x-9).

x/(x-18) + 11/(x-9) = x²/(x²-27x+162)

x/(x-18) + 11/(x-9) = x²/[(x-18)(x-9)]

x(x-9)/[(x-18)(x-9)] + 11(x-18)/[(x-18)(x-9)] = x²/[(x-18)(x-9)]

x(x-9) + 11(x-18) = x²

x² - 9x + 11x - 198 = x²

x² + 2x - 198 = x²

2x - 198 = 0

2x = 198

x = 99

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