Question

Help me simplify this! Steps!

Answer 1

\[\frac{ X+3 }{ \sqrt{x^{2}-9} }\]

Answer 2

both lower case xs

Answer 3

what does "simplify" mean in this case?

Answer 4

get rid of the square root in the denominator

Answer 5

then multiply top and bottom by \(\sqrt{x^2-9}\)

Answer 6

you will have a term to cancel after you do that

Answer 7

so I got X^4-18X^2+81 for the denominator

Answer 8

no

Answer 9

\[\sqrt{\heartsuit}\times \sqrt{\heartsuit}=\heartsuit\]

Answer 10

denominator is just the term inside the radical

Answer 11

or rather "expression"

Answer 12

You can also think of it as exponents to \[\sqrt{x} = x^{1/2}\]
\[\huge x^{1/2} \times x^{1/2} = x^{1/2+1/2} = x \]

Answer 13

got it!

Answer 14

then factor the difference of two squares you get in the denominator, then cancel with the common factor in the numerator

Answer 15

\[\frac{ \sqrt{X^2-9} }{ x-3 }\]

Answer 16

looks good to me

Answer 17

I get confused when I have to multiply by the opposite side? What instance would you use that? @satellite73

Answer 18

i guess when there is "another side" i take it you mean when you have an equation , rather than an expression

Answer 19

unless you mean when you have to multiply by the "conjugate" as in \[\frac{3}{\sqrt{2}+5}\]

Answer 20

Yup thats what I got confused on!

Answer 21

that expression has a radical and a whole number in the denominator
yours in this question only had a radical there

Answer 22

Thanks for the help @satellite73