Ответ:
x = 2
x = [tex]-\frac{21}{8}[/tex]
Объяснение:
[tex]\frac{5}{x^{2} + 3x} - \frac{15}{x^{2} - 3x} = \frac{16}{x}[/tex]
[tex]\frac{5(x-3)}{x(x+3)(x-3)} - \frac{15(x+3)}{x(x-3)(x+3)} - \frac{16(x-3)(x+3)}{x(x-3)(x+3)} = 0[/tex]
[tex]\frac{(5x - 15) - (15x + 45) - (16x^{2} - 144) }{x(x-3)(x+3)} = 0[/tex]
x ≠ 0
x ≠ 3
x ≠ -3
[tex]5x - 15 - 15x - 45 - 16x^{2} + 144 = 0[/tex]
[tex]-16x^{2} - 10x + 84 = 0[/tex]
[tex]8x^{2} + 5x - 42 =0[/tex]
[tex]D = b^2 - 4ac = 5^2 - 4*8*(-42) = 25 + 1344 = 37^{2}[/tex]
[tex]x_{1,2} = \frac{-b +- \sqrt{D} }{2a} = \frac{-5+- 37}{16}[/tex]
x₁ = 2
x₂ = [tex]-\frac{21}{8}[/tex]