Question 110020
1. {{{5/(x-2)- 5/(x+2)=4}}}.......... on left side , common denominator is {{{(x-2)(x+2)}}} 

{{{(5(x+2)- 5(x-2))/(x-2)(x+2)=4}}}..........multiply both sides by {{{(x-2)(x+2)}}}   

{{{(5(x+2)- 5(x-2))/(x-2)(x+2)* (x-2)(x+2) =4(x-2)(x+2) }}}..........

{{{(5(x+2)- 5(x-2)) =4(x-2)(x+2) }}}..........

{{{5((x+2)- (x-2)) =4(x-2)(x+2) }}}..........

{{{5(x+2 - x + 2) =4(x-2)(x+2) }}}..........

{{{5(2+ 2) =4(x-2)(x+2) }}}..........

{{{20 =4(x-2)(x+2) }}}..........divide both sides by {{{4}}}

{{{5 =(x-2)(x+2) }}}..........


{{{5 =x^2-2^2 }}}..........

{{{5 =x^2-4 }}}..........move {{{-4}}} to the left

{{{5 + 4 =x^2 }}}..........

or

{{{x^2 = 9}}}

{{{x[1]= + 3}}}

{{{x[2]= - 3}}}


2. {{{(x/3)-(x+2)/2 =1}}}........common denominator is {{{3*2=6}}}


{{{(2x-3*(x+2))/6 =1}}}........multiply both sides by {{{6}}}

{{{6*(2x-3*(x+2))/6 =1*6}}}........

{{{(2x-3*(x+2)) = 6}}}........

{{{(2x-3x -6) = 6}}}........

{{{-x -6 =6}}}........move {{{-6}}} to the right

{{{-x =6 + 6}}}........multiply both sides by {{{-1}}}

{{{x = -12}}}........