Question

Помогите решить уравнения:
/7х+5/=/3-7х/ ( модули )
7-1/х-2=-22/х-9

Answer 1

$1)quad |7x+5|=|3-7x|\\|7x+5|^2=|3-7x|^2; ; Leftrightarrow ; ; ; (7x+5)^2=(3-7x)^2\\(7x+5)^2-(3-7x)^2=0\\(7x+5-(3-7x))cdot (7x+5+(3-7x))=0\\(14x+2)cdot 8=0\\14x+2=0; |:2\\7x+1=0\\x=-frac{1}{7}$

$2)quad 7- frac{1}{x-2} =-frac{22}{x-9}; ,; ; ; ODZ:; xne 2,; xne 9\\ frac{7x-15}{x-2}+ frac{22}{x-9} =0\\ frac{(7x-15)(x-9)+22(x-2)}{(x-2)(x-9)} =0\\ frac{7x^2-78x+135+22x-44}{(x-2)(x-9)} =0\\ frac{7x^2-56x+91}{(x-2)(x-9)} =0\\7x^2-56x+91=0; |:7\\x^2-8x+13=0\\D/4=3; ,; ; x_1=4-sqrt3; ,; ; x_2=4+sqrt3; .$