Question

Under root A plus B plus under root A minus B divided by under root A plus B minus under root A minus B

Answer 1

Given :   Under root A plus B plus under root A minus B divided by under root A plus B minus under root A minus B

$\dfrac{\sqrt{A+B} +\sqrt{A-B}}{\sqrt{A+B} -\sqrt{A-B}}$

To Find : Simplify

Solution :

$\dfrac{\sqrt{A+B} +\sqrt{A-B}}{\sqrt{A+B} -\sqrt{A-B}}$

Rationalize

$\dfrac{\sqrt{A+B} +\sqrt{A-B}}{\sqrt{A+B} -\sqrt{A-B}} \times \dfrac{\sqrt{A+B} +\sqrt{A-B}}{\sqrt{A+B} +\sqrt{A-B}}$

use identity

(x + y)² = x²  + y² + 2xy

(x + y)(x - y) = x² - y²

(√x)² = x  

={ (A + B) + (A - B) + 2√(A² - B²) } / {A + B - (A - B) }

= {2A + 2√(A² - B²) } / 2B

=   { A +  √(A² - B²) } /  B

= $\dfrac{A +\sqrt{A^2-B^2}}{B}$

$\dfrac{\sqrt{A+B} +\sqrt{A-B}}{\sqrt{A+B} -\sqrt{A-B}} = \dfrac{A +\sqrt{A^2-B^2}}{B}$

Learn More:

simplify 6-4√3|/6+4√3 by rationalizing the denominator - Brainly.in

https://brainly.in/question/3963591

simplify √√30+√21/√30-√21​ - Brainly.in

https://brainly.in/question/25878266