Trouble with algebra at the end of an elasticity problem

[K29]

I have a spherical shell with inner radius $a_{1}$ and outer radius $a_{2}$

I have worked out that the tension at $r=a_{1}$ is
$\tau=\frac{2a_{1}^3+a_{2}^3}{2(a_{2}^{3}-a_{1}^{3})}P_{1}$

($P_{1}$ is pressure from the inside of the shell, causing the tension.

Now if the shell is not very thick. $t=a_{2}-a_{1}$ is small. $\frac{t}{a_1}<<1$

and I should be able to show

$\tau\approx\frac{a_{1}}{2t}P_{1}$

But I am not sure about the first step to take in getting there. Any ideas? Please help.

 

[TSny]

You can factor a difference of cubes.

 

[K29]

Thank you