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