1. Решить х-4/x=2x+10/x+4

(х-4)/х=(2х+10)/(х+4) (х+4)(х-4)=х(2х+10) х^2-16=2х^2+10х х^2+10х+16=0 D/4=25-16=9=±3^2 х1=5-3=2 х2=5+3=8

[latex] \frac{x-4}{x}= \frac{2x+10}{x} +4[/latex] [latex] \frac{x-4}{x}- \frac{2x+10}{x} -4=0[/latex] [latex] \frac{x-4-(2x+10)}{x}-\frac{4*x}{x} =0[/latex] [latex] \frac{x-4-2x-10}{x}-\frac{4x}{x} =0[/latex] [latex] \frac{-x-14}{x}-\frac{4x}{x} =0[/latex] [latex]- \frac{x+14}{x}-\frac{4x}{x} =0[/latex] [latex]\frac{x+14}{x}+\frac{4x}{x} =0[/latex] [latex]\frac{4x+x+14}{x}=0[/latex] [latex]\frac{5x+14}{x}=0[/latex] [latex] \left \{ {{5x+14=0} \atop {x \neq 0}} \right. ; \left \{ {{5x=-14} \atop {x \neq 0}} \right. ; \left \{ {{x=-\frac{14}{5}} \atop {x \neq 0}} \right. ; x=-\frac{14}{5}[/latex] Ответ: [latex]-\frac{14}{5}[/latex]