Rationalise the denominator- -a-x-a-x-a-x-a-x-

The correct option is C a+√(a^2 x^2)/x √(a+x)+√(a x)√(a+x) √(a x) =√(a+x)+√(a x)√(a+x) √(a x)×√(a+x)+√(a x)/√(a+x)+√(a x) =(√(a+x)+√(a x))^ ...

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Quadratic Formula

Rationalise t...

Question

Rationalise the denominator:
$\frac{\sqrt{a + x} + \sqrt{a - x}}{\sqrt{a + x} - \sqrt{a - x}}$ .

\frac{a - \sqrt{a^{2} - x^{2}}}{x}

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\frac{a + \sqrt{a^{2} + x^{2}}}{x}

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\frac{a - \sqrt{a^{2} + x^{2}}}{x}

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\frac{a + \sqrt{a^{2} - x^{2}}}{x}

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\int \frac{d x}{\sqrt{x^{2} + a^{2}}} = l n | x + \sqrt{x^{2} + a^{2}} | + C

\int \frac{d x}{\sqrt{x^{2} - a^{2}}} = l n | x - \sqrt{x^{2} - a^{2}} | + C

\int \frac{d x}{x^{2} - a^{2}} = \frac{1}{2 a} l n ∣ ∣ \frac{x - a}{x + a} ∣ ∣ + C

\int \frac{d x}{a^{2} - x^{2}} = \frac{1}{2 a} l n ∣ ∣ \frac{x + a}{x - a} ∣ ∣ + C

\int \frac{x \sqrt{a^{2} - x^{2}}}{a^{2} + x^{2}} d x = \sqrt{a^{2} - x^{2}} - \frac{a}{\sqrt{(2)}} log \frac{a \sqrt{2} + \sqrt{a^{2} - x^{2}}}{a \sqrt{(2)} - \sqrt{(a^{2} - x^{2})}}

\frac{\sqrt{a^{2} + a x + x^{2}} - \sqrt{a^{2} - a x + x^{2}}}{\sqrt{a + x} - \sqrt{a - x}},

x = 0

l i m x \to 0 \frac{\sqrt{a^{2} - a x + x^{2}} - \sqrt{a^{2} + a x + x^{2}}}{\sqrt{a + x} - \sqrt{a - x}}

lim x \to 0 f (x)

f (x) = \frac{\sqrt{a^{2} - a x + x^{2}} - \sqrt{a^{2} + a x + x^{2}}}{\sqrt{a + x} - \sqrt{a - x}}

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