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Special Quotients


Definition

Special quotients are those quotients that can be obtained directly or simply by inspection, without the need to perform the division operation or factorization.


Problems Solved

$\frac{\left(m^2-n^2\right)}{m+n}$
$\frac{x^4-y^4}{x+y}$
$\frac{\sin^2x}{1+\cos x}$
Prove the identity $\frac{cos^2x}{1-\sin\left(x\right)}=1+\sin\left(x\right)$
$\frac{m^4-16}{m+2}$
Prove the identity $\frac{\left(1+csc\:x\right)}{csc\:x}=\frac{\left(cos^2\:x\right)}{1-sin\:x}$
$\frac{\left(2^2-x^2\right)}{2+x}$

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