Answer:
Step-by-step explanation:
put (x+2)/(x-2)=a
a-1/a=5/6
[tex]multiply~by~6a \\6a^2-6=5a\\6a^2-5a-6=0\\6a^2-9a+4a-6=0\\3a(2a-3)+2(2a-3)=0\\(2a-3)(3a+2)=0\\either 2a-3=0,a=3/2 \\\frac{x+2}{x-2} =\frac{3}{2} \\cross~multiply\\3x-6=2x+4\\3x-2x=4+6\\x=10\\[/tex]
[tex]or~3a+2=0\\a=-2/3\\\frac{x+2}{x-2} =-\frac{2}{3} \\3x+6=-2x+4\\3x+2x=4-6\\5x=-2\\x=-2/5[/tex]
2.
put (x+3)/x=a
a+1/a=4 1/4
[tex]a+\frac{1}{a} =\frac{17}{4} \\multiply~by~4a\\4a^2+4=17a\\4a^2-17a+4=0\\4a^2-16a-a+4=0\\4a(a-4)-1(a-4)=0\\(a-4)(4a-1)=0\\either~a-4=0,a=4\\\frac{x+3}{x} =4\\4x=x+3\\4x-x=3\\3x=3\\x=3/3=1\\or\\4a-1=0\\a=1/4\\\\\frac{x+4}{x} =\frac{1}{4} \\4x+16=x\\3x=-16\\x=-16/3[/tex]
