Question

Rationalize the numerator: (square root of (x+4) - square root of (3x-6) )/ x-5

Answer 1

multiply top and bottom by sqrt(x+4)+sqrt(3x-6)

Answer 2

ive gone that far, i get stuck in the simplification. ive have gotten x+4-3x+6 / (x-5) (sqrt(x+4)+sqrt(3x-6) ) which seems to be wrong

Answer 3

nice start
(-2x+10) / [(x-5) (sqrt(x+4)+sqrt(3x-6) )]
numerator can be -2(x-5) and cancel with the same (x-5) in the denominator.
and you are left with
-2 / (sqrt(x+4)+sqrt(3x-6) )

Answer 4

Thank you so much!

Answer 5

That works, dizliz. The reason you can use x or y is because you can draw a triangle on a coordinate plane (or a graph as it's more commonly called). But it's a good idea to remember opposite/hypotenus/adjacent as that's how triangles are more commonly encountered. A trick to remember them:

cos without the o is cs. cs sounds like x. So it's x/hypotenuse.
sin sounds like sYn. So sine is Y/hypotenuse.

:)