If frac{x^2}{(x^2 + a^2)(x^2 + b^2)} = K left | vedclass

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(D) Let $u = x^2$. The expression becomes $\frac{u}{(u + a^2)(u + b^2)} = K \left( \frac{a^2}{u + a^2} - \frac{b^2}{u + b^2} \right)$.Expanding the ri

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$\frac{1}{a^2 - b^2}$

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(D) Let $u = x^2$. The expression becomes $\frac{u}{(u + a^2)(u + b^2)} = K \left( \frac{a^2}{u + a^2} - \frac{b^2}{u + b^2} \right)$.Expanding the right side: $K \left( \frac{a^2(u + b^2) - b^2(u + a^2)}{(u + a^2)(u + b^2)} \right) = K \left( \frac{a^2u + a^2b^2 - b^2u - a^2b^2}{(u + a^2)(u + b^2)} \right)$.This simplifies to $K \left( \frac{u(a^2 - b^2)}{(u + a^2)(u + b^2)} \right)$.Equating the numerators: $u = K u (a^2 - b^2)$.Dividing both sides by $u(a^2 - b^2)$,we get $K = \frac{1}{a^2 - b^2}$.

If $\frac{x^2}{(x^2 + a^2)(x^2 + b^2)} = K \left( \frac{a^2}{x^2 + a^2} - \frac{b^2}{x^2 + b^2} \right)$,then $K =$

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