Andrew,
Simplifying this variable expression is very much like simplifying the fraction 810/225 . With this fraction I would probably first notice that 5 divides both the numerator and denominator, so dividing both by 5 I get
810/225 = 162/45
Now I notice that 9 divides both the numerator and denominator, so dividing both by 9 I get
810/225 = 162/45 = 18/5
There are no further common factors in the numerator and denominator so my answer is
810/225 = 18/5
The technique is similar with 3g2h over 12gh. First I notice that there is a common factor of h in the numerator and denominator. Hence
3g2h/12gh = 3g2/12g
Next there is a g common factor in the numerator and denominator so
3g2h/12gh = 3g2/12g = 3g/12
Finally 3 divides both the numerator and denominator so
3g2h/12gh = 3g2/12g = 3g/12 = g/4
Penny
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