Question 552200
<pre>
{{{a/(bx)}}} + {{{c/d}}} = e

{{{a/(bx)}}} + {{{c/d}}} = {{{e/1}}}

To clear of fractions, multiply through by LCD of {{{red(((bdx)/1))}}}

{{{red(((bdx)/1))}}}{{{a/(bx)}}} + {{{red(((bdx)/1))}}}{{{c/d}}} = {{{red(((bdx)/1))}}}{{{e/1}}}

{{{red(((cross(b)d*cross(x))/1))}}}{{{a/(cross(b)cross(x))}}} + {{{red(((b*cross(d)x)/1))}}}{{{c/cross(d)}}} = {{{red(((bdx)/1))}}}{{{e/1}}}

da + bxc = bdxe

Get all terms in x on the right by subtracting bxc from both sides:

      da = bdxe - bxc

Factor bx out of the right side:

      da = bx(de - c)

Divide both sides by b(de - c)

{{{da/(b(de-c))}}} = {{{(bx(de-c))/(b(de-c))}}}

{{{da/(b(de-c))}}} = {{{(cross(b)x(cross(de-c)))/(cross(b)(cross(de-c)))}}}

{{{da/(b(de-c))}}} = x

x = {{{da/(b(de-c))}}} 

Edwin</pre>