Question 725423
{{{(15/16)b=5/12}}}
Divide both sides by {{{15/16}}} , which is the same as multiplying times {{{16/15}}} .
{{{(15/16)b(16/15)=(5/12)(16/15)}}} --> {{{(15*16/16/15)b=5*16/12/15}}} --> {{{(1)b=5*4*4/3/4/3/5}}} --> {{{(1)b=5*4*4/5/4/3/3}}} --> {{{(1)b=(5/5)*(4/4)*(4/3/3)}}} --> {{{b=(1)*(1)*(4/9)}}} --> {{{highlight(b=4/9)}}}
 
NOTE:
You do not need to write all of
{{{(15/16)b(16/15)=(5/12)(16/15)}}} --> {{{(15*16/16/15)b=5*16/12/15}}} --> {{{(1)b=5*4*4/3/4/3/5}}} --> {{{(1)b=5*4*4/5/4/3/3}}} --> {{{(1)b=(5/5)*(4/4)*(4/3/3)}}} --> {{{b=(1)*(1)*(4/9)}}} --> {{{highlight(b=4/9)}}}
For your teacher, {{{(15/16)b(16/15)=(5/12)(16/15)}}} --> {{{highlight(b=4/9)}}} may be enough.
At most your teacher may want to see some cancelling out of factors that is easy to scribble on paper, but I would not know how to type here.
In any case the crossing out of those factors is not algebra voodoo magic. It is the rearranging to give those (1) factors.