To perform the indicated operations with the given expression, we need to follow the order of operations.
First, we need to simplify 6+3g in the denominator of the first fraction.
Then, we need to divide 10-5g by the result from the first step.
Finally, we need to multiply by the result of the fraction in the numerator.
So the solution is:
(10-5g)/((6+3g)/(5/12+6g))
We can simplify the denominator further by finding a common denominator for 5/12 and 6g. A common denominator is 12, so we multiply 5/12 by 1 = 12/12 and 6g by 2 = 24/12. Then we get:
(10-5g)/((6+3g)/(12/12+24g/12))
(10-5g)/((6+3g)/(36g+12)/12))
(10-5g)/(6+3g)*(12)/(36g+12)
(10-5g)/3(2+g)*12/12(3g+1)
(10-5g)/3(2+g)*(3g+1)
So the final solution is:
(10-5g)(3g+1)/(3(2+g))
or
(5g-10)(3g+1)/(3(g+2))