Question 180496
{{{((3x-6))/((2-x))}}} = {{{3/2}}}
Cross multiply
2(3x-6) = 3(2-x)
:
6x - 12 = 6 - 3x
:
6x + 3x = 6 + 12
;
9x = 18
x = {{{18/9}}}
x = 2, however there is no solution, as x=2 causes division by 0
:
:
{{{8/((z-2))}}} = {{{((z+2))/4}}}
Cross multiply
(z-2)*(z+2) = 8 * 4
:
FOIL
z^2 + 2z - 2z - 4 = 32
:
z^2 - 4 - 32 = 0
:
z^2 - 36 = 0
The difference of squares factors to:
(z-6)(x+6) = 0
z = +6
z = -6
:
:
Check solutions in original equation
z = 6
{{{8/((6-2))}}} = {{{((6+2))/4}}}
{{{8/4}}} = {{{8/4}}}
:
z = -6
{{{8/((-6-2))}}} = {{{((-6+2))/4}}}
{{{8/(-8)}}} = {{{(-4)/4}}}
-1 = -1