Question 81644
The restrictions in this case is that x cannot equal to zero because you cannot divide by zero.
{{{(4/x)}}} = {{{(5/x - 1/2)}}} 
{{{((2x)4/x)}}} = {{{((2x)5/x - (2x)1/2)}}} [find the LCD (2x); multiply each term by the LCD]
.
8=10-x [cancel wherever possible]
8=10-x [solve for the x-term]
8-8=10-8-x
0=2-x
-2=2-2-x
-2=-x
-2/-1=-x/-1
2=x
.
check by plugging (x=2) back into the original equation and solve:
{{{(4/x)}}} = {{{(5/x - 1/2)}}}
{{{(4/2)}}} = {{{(5/2 - 1/2)}}}
2={{{(4/2)}}}
2=2 [checks out]