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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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^

Vedclass · Accepted Answer

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

Vedclass · Answer

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

Similar Questions

If $a+b+c=1$ and $ab+bc+ca=\frac{1}{3}$,then $a:b:c$ is

What is the value of $\frac{2.75 \times 2.75 \times 2.75 - 2.25 \times 2.25 \times 2.25}{2.75 \times 2.75 + 2.75 \times 2.25 + 2.25 \times 2.25}$?

$3.75 + 2.832 - 1.001 + 1.803 = ?$

If $5 \sqrt{5} \times 5^{3} \div 5^{-\frac{3}{2}} = 5^{a+2},$ then the value of $a$ is

If $3x + \frac{3}{x} = 1$,then $x^{3} + \frac{1}{x^{3}} + 1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

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