How do you simplify #(a^2-b^2)/(4b) div (a-b)/(36b^2)#?

Question

1324 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-07T09:15:04

#a²-b²=(a+b)(a-b)#
And #36b²=4b*9b#

Thus :
#(a^2−b^2)/(4b)÷(a−b)/(36b^2)=((a+b)(a-b))/(4b)÷(a-b)/(4b*9b)#

And we know that dividing by #a/b# is the same thing as multiplying by #b/a#

Thus :

#=((a+b)(a-b))/(4b)*(4b*9b)/((a-b)#

#=((a+b)cancel((a-b)))/cancel(4b)*(cancel(4b)*9b)/(cancel((a-b)#

#=(a+b)*9b#

#=9ba+9b²#