How do you evaluate #\frac { 10c d } { 3d ^ { 2} } \div \frac { 12c ^ { 3} } { 6d }#?

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Answer 1 · 2017-12-10T10:41:37

#color(blue)(5/(3c^2)#

The expression given to us is

#color(blue)((10cd)/(3d^2) -: (12c^3)/(6d)# #color(green)(Expression.1)#

We know that

#color(red)(a/b-:c/d hArr a/b*d/c)# ....... Formula.1

We will write #color(green)(Expression.1)# using ....... Formula.1 as

#color(blue)((10cd)/(3d^2) X (6d)/(12c^3)# #color(green)(Expression.2)#

We can group the like terms in #color(green)(Expression.2)#

#rArr [(10* 6)/(3*12)][c/c^3][(d*d)/(d^2)]#

Simplify to get

#rArr [(60)/(36)][1/c^2][(d^2)/(d^2)]#

Further simplification yields

#rArr [(5)/(3)][1/c^2][cancel (d^2)/cancel( d^2)]#

Hence,

#color(blue)(5/(3c^2))# is our final answer.

I hope you find this solution process useful.