Question 118069
I'll do the first two to help you get started


#1



{{{5cd/(10c/d)}}} Start with the given expression



{{{(5cd/1)/(10c/d)}}} Rewrite {{{5cd}}} as {{{5cd/1}}}


{{{(5cd/1)*((d)/(10c))}}} Multiply the first fraction by the reciprocal of the second fraction



{{{(5cd*d)/(10c)}}} Combine the fractions



{{{(5cd*d)/(2*5c)}}} Factor 10 into 2*5



{{{(cross(5)cross(c)d*d)/(2*cross(5)cross(c))}}} Cancel like terms



{{{d^2/2}}} Simplify



So {{{5cd/(10c/d)}}}  simplifies to {{{d^2/2}}}



<hr>



#2



{{{((b^2)/(b-6))/((b)/(b-6))}}} Start with the given expression




{{{((b^2)/(b-6))*(((b-6))/((b)))}}} Multiply the first fraction by the reciprocal of the second fraction




{{{((b*b)/(b-6))*(((b-6))/((b)))}}} Factor {{{b^2}}} into {{{b*b}}}



{{{((cross((b))*b)/cross((b-6)))*((cross((b-6)))/(cross((b))))}}} Cancel like terms



{{{b}}} Simplify




So {{{((b^2)/(b-6))/((b)/(b-6))}}}  simplifies to {{{b}}}