Question

HELP WILL GIVE BRAINLESS Which choice is equivalent to the fraction below? (Hint: Rationalize the

denominator and simplify.)
2
√x + √x+ 2
2
A. VX + 1x + 2
B. FxVx+ 2
C. x + 2 - 3

Answer 1

C.
`√(x + 2) - √(x)`

Explanation:

`(2)/( √(x) + √(x + 2) ) \\ \\ = (2)/( (√(x) + √(x + 2)) ) * ((√(x) - √(x + 2)))/((√(x) - √(x + 2))) \\ \\ = \frac{2( √(x) - √(x + 2)) }{ ({ √(x) )}^(2) - {( √(x + 2) )}^(2) } \\ \\ = \frac{2( √(x) - √(x + 2)) }{ x - {( x + 2)} } \\ \\ = (2( √(x) - √(x + 2)) )/( x - x - 2 ) \\ \\ = (2( √(x) - √(x + 2)) )/( - 2 ) \\ \\ = - ( √(x) - √(x + 2)) \\ \\ (2)/( √(x) + √(x + 2) ) = \purple{ \bold{√(x + 2) - √(x) }}`