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

Jun 7, 2015

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 $\frac{a}{b}$ is the same thing as multiplying by $\frac{b}{a}$

Thus :

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

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

$= \left(a + b\right) \cdot 9 b$

=9ba+9b²