Using theorem of componento- dividendo, solve the equation x+3+x−3x+3−x−3=43.x+3+x−3x+3−x−3=43.\frac{\sqrt{x + 3} + \sqrt{x - 3}}{\sqrt{x + 3} - \sqrt{x - 3}} = \frac{4}{3}.x+3−x−3x+3+x−3=34.x+3−x−3x+3+x−3=34.
Solution: Given equation is x+3+x−3x+3−x−3=43x+3+x−3x+3−x−3=43\frac{\sqrt{x + 3} + \sqrt{x - 3}}{\sqrt{x + 3} - \sqrt{x - 3}} = \frac{4}{3}x+3−x−3x+3+x−3=34x+3−x−3x+3+x−3=34
By componento- dividendo theorem
x+3+x−3+x+3−x−3x+3+x−3−x+3+x−3=4+34−3x+3+x−3+x+3−x−3x+3+x−3−x+3+x−3=4+34−3\frac{\sqrt{x + 3} + \sqrt{x - 3} + \sqrt{x + 3} - \sqrt{x - 3}}{\sqrt{x + 3} + \sqrt{x - 3} - \sqrt{x + 3} + \sqrt{x - 3}} = \frac{4 + 3}{4 - 3}x+3+x−3−x+3+x−3x+3+x−3+x+3−x−3=4−34+3x+3+x−3−x+3+x−3x+3+x−3+x+3−x−3=4−34+3