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Indeterminate Forms

Simplify the ...

Question

Simplify the following algebraic expressions.

$\frac{x^{2} + a^{2}}{a b} + \frac{x - a}{a x} - \frac{x^{3}}{b}$

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Solution

$\frac{x^{2} + a^{2}}{a b} + \frac{x - a}{a x} - \frac{x^{3}}{b}$
$= \frac{(x^{2} + a^{2}) x + b (x - a) - x^{3} (a x)}{a b x}$
$= \frac{x^{3} + a^{2} x + b x - b a - a x^{4}}{a b x}$
Therefore, $\frac{x^{2} + a^{2}}{a b} + \frac{x - a}{a x} - \frac{x^{3}}{b} = \frac{x^{3} + a^{2} x + b x - b a - a x^{4}}{a b x}$

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