Answer:
[tex]\frac{9}{a - b}[/tex].
Step-by-step explanation:
a^2 - b^2 = 9
(a + b)(a - b) = 9
a + b = [tex]\frac{9}{a - b}[/tex].
ab = 3
a = 3/b
3/b + b = [tex]\frac{9}{\frac{3}{b} -b}[/tex]
3 + b^2 = [tex]\frac{9b}{\frac{3}{b}-\frac{b^2}{b} }[/tex]
3 + b^2 = [tex]\frac{9b}{\frac{3-b^2}{b} }[/tex]
3 + b^2 = [tex]9b * \frac{b}{-b^2 + 3}[/tex]
3 + b^2 = [tex]\frac{9b^2}{-b^2 + 3}[/tex]
(b^2 + 3)(-b^2 + 3) = 9b^2
-b^4 + 9 = 9b^2
b^4 + 9b^2 - 9 = 0
Let's say that b^2 = x
x^2 + 9x - 9 = 0
Hope this [somewhat] helps!
