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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

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

Vedclass · Answer

(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 $K =$

Similar Questions

Foetal ejection reflex in human female is induced by

In prokaryotes,chromatophores are

In a food chain,the total amount of living material is depicted by

If a normal chord at a point $t$ on the parabola $y^2=4ax$ subtends a right angle at the vertex,then $t^2$ equals to

$A$ horizontal force of $10\,N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and wall is $0.2$. The weight of the block is ........ $N$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module