4целых 2/9x+3целых 5/14=6целых 11/21

4²/₉ x + 3⁵/₁₄ = 6¹¹/₂₁;

4²/₉ х = 6¹¹/₂₁ - 3⁵/₁₄;

6¹¹/₂₁ - 3⁵/₁₄ = 6 ^{11* 2}/_{21 * 2} - 3 ^{5 * 3}/_{14 * 3} = 6²²/₄₂ - 3¹⁵/₄₂ = (6 - 3) + (^{22 - 15}/₄₂) =

 = 3 + ⁷/₄₂ = 3¹/₆;

4²/₉х = 3¹/₆;

х = 3¹/₆ : 4²/₉;

х =¹⁹/₆ : ³⁸/₉;

х = ¹⁹/₆ * ⁹/₃₈;

х = ^{19 * 9}/_{6 * 38};

х = ¹/₄;

х = 0,25.

Ответ: х = 0,25.