Simplify:frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+frac | vedclass

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(D) Given expression: $\frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+\frac{1-a^{-1 / 2}}{1+a^{1 / 2}}$Step $1$: Factor the denominator $(1-a)$ as $(1-a^{1/2})(1+a^

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

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(D) Given expression: $\frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+\frac{1-a^{-1 / 2}}{1+a^{1 / 2}}$Step $1$: Factor the denominator $(1-a)$ as $(1-a^{1/2})(1+a^{1/2})$.Step $2$: Find a common denominator,which is $(1-a^{1/2})(1+a^{1/2}) = 1-a$.Step $3$: Combine the fractions:$= \frac{a^{1/2} + a^{-1/2} + (1 - a^{-1/2})(1 - a^{1/2})}{1 - a}$Step $4$: Expand the numerator term $(1 - a^{-1/2})(1 - a^{1/2})$:$= 1 - a^{1/2} - a^{-1/2} + a^{(-1/2 + 1/2)} = 1 - a^{1/2} - a^{-1/2} + 1 = 2 - a^{1/2} - a^{-1/2}$.Step $5$: Substitute back into the expression:$= \frac{a^{1/2} + a^{-1/2} + 2 - a^{1/2} - a^{-1/2}}{1 - a}$Step $6$: Simplify the numerator:$= \frac{2}{1 - a}$.

Simplify:
$\frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+\frac{1-a^{-1 / 2}}{1+\sqrt{a}}$

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Simplify:$\frac{a^{1 / 2}+a^{-1 / 2}}{1-a}+\frac{1-a^{-1 / 2}}{1+\sqrt{a}}$