Решите уравнение:[latex] \frac{x^{2} - 2x}{4x-3} + 5 = \frac{16x-12}{2x-x^2} [/latex]

[latex]\frac{x^2-2x}{4x-3}+5=\frac{16x-12}{2x-x^2}\\\\ zamena \\ x^2-2x=a\\ 4x-3=b\\\\ \frac{a}{b}+5=\frac{4b}{-a}\\ \frac{a+5b}{b}=\frac{-4b}{a}\\ a^2+5ab=-4b^2\\ a^2+4b^2+5ab=0\\ (b+a)(4b+a)=0\\ a=-b\\ a=-4b\\\\ x^2-2x=3-4x\\ x^2+2x-3=0\\ D=4^2\\ x=1;-3\\\\ x^2-2x=4(3-4x)\\ x^2-2x=12-16x\\ x^2+14x-12=0\\ D=196+4*1*12=\sqrt{244}^2\\ x=\frac{-14+/-\sqrt{244}}{2}[/latex]