How do you find the quotient of #(6b-12)/(b+5)div(12b+18)#?

Question

Eli Assouline · Accepted Answer

#=frac{b-2}{(b+5)(2b+3)}# #frac{6b-12}{b+5}divide(12b+18)# #frac{(6b-12)}{(b+5)}*frac{1}{(12b+18)}# Factor the terms completely: #=frac{color(red)((6))(b-2)}{(b+5)}*frac{1}{color(red)((6))(2b+3)}# #=frac{b-2}{(b+5)(2b+3)}#

Hazel Anglin · Answer

undefined To find the quotient of (6b-12)/(b+5) divided by (12b+18), we can follow these steps:

1. Simplify the expression (6b-12)/(b+5) by factoring out the greatest common factor, which is 6:
   (6b-12)/(b+5) = 6(b-2)/(b+5)

2. Simplify the expression (12b+18) by factoring out the greatest common factor, which is 6:
   (12b+18) = 6(2b+3)

3. Now, we can rewrite the division expression as a multiplication by taking the reciprocal of the divisor:
   6(b-2)/(b+5) ÷ 6(2b+3) = 6(b-2)/(b+5) * 1/(6(2b+3))

4. Simplify the expression by canceling out common factors:
   6(b-2)/(b+5) * 1/(6(2b+3)) = (b-2)/(b+5) * 1/(2b+3)

Therefore, the quotient of (6b-12)/(b+5) divided by (12b+18) is (b-2)/(b+5) * 1/(2b+3).