Rational,20 $$ \frac{\sqrt{1+x}+\sqrt{x}}{\sqrt{1}+x-\sqrt{x}} $$

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Romero Rowe · Accepted Answer

To rationalize the expression $$ \frac{\sqrt{1+x} + \sqrt{x}}{1 + x - \sqrt{x}} $$, multiply both the numerator and the denominator by the conjugate $$1 + x + \sqrt{x}$$. This results in: $$ \frac{(\sqrt{1+x} + \sqrt{x})(1 + x + \sqrt{x})}{(1 + x - \sqrt{x})(1 + x + \sqrt{x})} = \frac{(\sqrt{1+x} + \sqrt{x})(1 + x + \sqrt{x})}{1 + x + x^2} $$ The rationalized form is: $$ \frac{(\sqrt{1+x} + \sqrt{x})(1 + x + \sqrt{x})}{1 + x + x^2} $$

Rational,20 \( \frac{\sqrt{1+x}+\sqrt{x}}{\sqrt{1}+x-\sqrt{x}} \)

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Rational,20 \( \frac{\sqrt{1+x}+\sqrt{x}}{\sqrt{1}+x-\sqrt{x}} \)

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