Question

(4x)/(\sqrt(3x+11))

rationalize the denominator.

Answer 1

times whole thing by
`( √(3x+11) )/( √(3x+11) )`
we get

`(4 √(3x+11) )/(3x+11)`

Answer 2

so called "rationalizing" it, is just getting rid of the pesky radical at the bottom

so
`\bf \cfrac{4x}{√(3x+11)}\cdot \cfrac{√(3x+11)}{√(3x+11)}\implies \cfrac{4x√(3x+11)}{(√(3x+11))^2}\iff \cfrac{4x√(3x+11)}{√((3x+11)^2)} \\\\\\ \cfrac{4x√(3x+11)}{3x+11}`