Multiplying and Dividing Rational Expressions, in Depth

If $a$ and $b$ are nonzero real numbers such that $\left| a \right| \ne \left| b \right|$, compute the value of the expression $$\left(\frac{b^2}{a^2}+\frac{a^2}{b^2}-2\right)\times\left(\frac{a+b}{b-a}+\frac{b-a}{a+b}\right)\times\left(\frac{\frac{1}{a^2}+\frac{1}{b^2}}{\frac{1}{b^2}-\frac{1}{a^2}}-\frac{\frac{1}{b^2}-\frac{1}{a^2}}{\frac{1}{a^2}+\frac{1}{b^2}}\right)$$

Source: Math Prize for Girls