Решите уравнение:
a) 5/x = 2 - 3/(x-2); б) 3/(2x-1) = 5x - 9.

Решение:





+ 5 = 0; D₁ = 9 - 5 = 4; x = 3 ± 2; x₁ = 5; x₂ = 1;
б) 3/(2x-1) = 5x - 9; 3 = (5x - 9)(2x - 1); 10x² - 5x - 18x + 9 - 3 = 0; 10x² - 23x + 6 = 0;
D = 23² - 4 • 6 • 10 = 529 - 240 = 289; x = (23±17)/20; x₁ = 2; x₂ = 0,3.