Question 167944
2p+18q divided by 9p-63q (all divided by) 10p+90q divided 8p-56q
<pre><font size = 4 color = "indigo"><b>
{{{matrix(1,3,(2p+18q)/(9p-63q), "÷", (10p+90q)/(8p-56q) )}}}

Invert the second fraction and change the division to multiplication:

{{{matrix(1,3,(2p+18q)/(9p-63q), "×",(8p-56q)/(10p+90q) )}}}

Factor out the greatest common divisor in all numerators
and denominators:

{{{matrix(1,3,(2(p+9q))/(9(p-7q)), "×",(8(p-7q))/(10(p+9q)) )}}}

Indicate the multiplication of the numerators and denominators:

{{{(2(p+9q)8(p-7q))/  (9(p-7q)10(p+9q) )}}}

Cancel the {{{(p+9q)}}}'s:

{{{(2cross((p+9q))8(p-7q))/  (9(p-7q)10cross((p+9q)) )}}}

Cancel the {{{(p-7q)}}}'s:

{{{(2cross((p+9q))8cross((p-7q)))/  (9cross((p-7q))10cross((p+9q)) )}}}

All that's left is

{{{(2*8)/(9*10)}}}

Cancel the {{{2}}} into the {{{10}}} and get {{{5}}}:

{{{(cross(2)*8)/(9*cross(10))}}}
   {{{5}}}

{{{8/(9*5)}}}

{{{8/45}}}

Edwin</pre>