Question

HELP MEMEMEME PLEELELELSESE Which choice is equivalent to the fraction below? (Hint: Rationalize the denominator and simplify)

Answer 1

so keeping in mind that a conjugate of a binomial is simply the same thing with a different sign, so "a + b" has a conjugate of "a - b" and so on, that said, let's use the conjugate of the denominator and multiply top and bottom by it.

`\cfrac{3}{√(x+3)-√(x)}\cdot \cfrac{√(x+3)+√(x)}{√(x+3)+√(x)}\implies \cfrac{3(√(x+3)+√(x))}{\underset{ \textit{difference of squares} }{(√(x+3)-√(x))(√(x+3)+√(x))}} \\\\\\ \cfrac{3(√(x+3)+√(x))}{(√(x+3))^2 ~~ - ~~ (√(x))^2}\implies \cfrac{3(√(x+3)+√(x))}{(x+3)~~ - ~~x} \\\\\\ \cfrac{3(√(x+3)+√(x))}{3}\implies √(x+3)+√(x)\implies √(x)+√(x+3)`