```Question 315337
<pre><b>
{{{1/x+2/(3x)=1/3}}}

Put parentheses around every term:

{{{(1/x)+(2/(3x))=(1/3)}}}

Multiply every term through by {{{LCD=red((3*x)/1)}}}

{{{red((3*x)/1)(1/x)+red((3*x)/1)(2/(3x))=red((3*x)/1)(1/3)}}}

Do some cancelling:

{{{red((3cross(x))/1)(1/cross(x))+red((cross(3)cross(x))/1)(2/(cross(3)cross(x)))=red((cross(3)x)/1)(1/cross(3))}}}

All that's left is

{{{3+2=x}}}

{{{5=x}}}

Checking:

{{{(1/x)+(2/(3x))=(1/3)}}}
{{{(1/5)+(2/(3*5))=(1/3)}}}
{{{1/5+2/15=1/3}}}
{{{3/15+2/15=1/3}}}
{{{5/15=1/3}}}
{{{1/3=1/3}}}

----------------------------

{{{5/(4x)+2=1/x)}}}

Put parentheses around every term and write the {{{2}}} as {{{2/1}}}:

{{{(5/(4x))+(2/1)=(1/x)}}}

Multiply every term through by {{{LCD=red((4*x)/1)}}}

{{{red((4*x)/1)(5/(4x))+red((4*x)/1)(2/1)=red((4*x)/1)(1/x)}}}

Do some cancelling:

{{{red((cross(4)cross(x))/1)(5/(cross(4)cross(x)))+8x/1=red((4cross(x))/1)(1/cross(x))}}}

All that's left is

{{{5+8x=4}}}

{{{8x=-1}}}

{{{x=(-1)/8}}}

{{{x=-1/8}}}

Edwin</pre>```