How do you multiply #(m+3)/(4m) div (m^2-9)/(32m^2(m-3))#?

Question

Genesis Allen · Accepted Answer

we are given :
# (m+3)/(4m)# / #(m^2-9)/(32m^2(m-3)# for multiplying we take the reciprocal of the second term: # = (m+3)/(4m)#  #xx# #32m^2xx(m-3)/(m^2-9)# we can write 
#m^2-9# as #(m+3)(m-3)# #= (m+3)/(4m)#  #xx# #32m^2xx(m-3)/((m+3)(m-3)# #= cancel(m+3)/(4m)#  #xx# #32m^2xxcancel(m-3)/(cancel(m+3)cancel(m-3)# #= (32m^2) / (4m)# #= 8m#

Kennedy Adams · Answer

undefined To multiply fractions, you need to multiply the numerators together and the denominators together.

For the given expression, (m+3)/(4m) divided by (m^2-9)/(32m^2(m-3)), the multiplication can be done as follows:

[(m+3)/(4m)] * [32m^2(m-3)/(m^2-9)]

Multiplying the numerators gives:

(m+3) * 32m^2(m-3)

Multiplying the denominators gives:

4m * (m^2-9)

Combining the terms, we get:

32m^3(m-3)(m+3) / 4m(m^2-9)

Simplifying further:

8m^2(m-3)(m+3) / (m(m+3)(m-3))

Canceling out common factors:

8m^2 / m

The final answer is:

8m