How do you find the quotient of #(3a)/(a^2+2a+1)div(a-1)/(a+1)#?

Question

Abigail Allen · Accepted Answer

#(3a)/((a+1)(a-1))# #"factor the denominator of the fraction on the left"# #"Change division to multiplication and turn the fraction"# #"on the right upside down. Perform any cancelling"# #=(3a)/((a+1)cancel((a+1)))xxcancel((a+1))/(a-1)# #=(3a)/((a+1)(a-1))=(3a)/(a^2-1)#

Eva Abramson · Answer

#(3a)/(a^2-1)# #(3a)/(a^2+2a+1)/((a-1)/(a+1))# =#(3a)/(a^2+2a+1)*(a+1)/(a-1)# =#(3a)/(a+1)^2*(a+1)/(a-1)# =#(3a)/((a+1)*(a-1))# =#(3a)/(a^2-1)#

Eli Assouline · Answer

undefined To find the quotient of (3a)/(a^2+2a+1) divided by (a-1)/(a+1), we can simplify the expression by multiplying the numerator by the reciprocal of the denominator.

First, let's simplify the expression (a-1)/(a+1) by multiplying both the numerator and denominator by (a-1). This gives us (a-1)^2 in the denominator.

Next, we can multiply the numerator (3a) by the reciprocal of the denominator, which is (a+1)/(a-1)^2.

Multiplying (3a) by (a+1) gives us 3a(a+1), and multiplying (a-1)^2 by (a-1) gives us (a-1)^3.

Therefore, the quotient is (3a(a+1))/((a-1)^3).