Question 313821
{{{4/(x+2)}}} - {{{6/(x-2)}}} = {{{6/(x^2-4)}}}
The right denominator is the difference of squares, factors to:
{{{4/(x+2)}}} - {{{6/(x-2)}}} = {{{6/((x-2)(x+2))}}}
Multiply each term by (x-2)(x+2), cancels the denominators, leaving:
4(x-2) - 6(x+2) = 6
:
4x - 8 - 6x - 12 = 6
:
-2x - 20 = 6
:
-2x = 6 + 20
:
-2x = 26
:
x = {{{26/(-2)}}}
x = -13
:
:
Check solution in original equation
{{{4/(x+2)}}} - {{{6/(x-2)}}} = {{{6/(x^2-4)}}}
x=-13
{{{4/(-13+2)}}} - {{{6/(-13-2)}}} = {{{6/(-13^2-4)}}}
:
{{{4/(-11)}}} - {{{6/(-15)}}} = {{{6/(169-4)}}}
-.36 - (-.4) = .04
-.36 + .40 = .04