Question

College Algebra Question:

Answer 1

So I know how to do both, its just giving an answer about how they are similar is what has me stumped

Answer 2

hint: conjugate

Answer 3

That hint doesn't really help

Answer 4

\[\text{ simplify } \frac{1}{\sqrt{2}-3} \text{ and also simplfy } \frac{1-i}{2+i}\]
not sure how it doesn't since that is what you to need to simplify both of these
you need to multiply both top and bottom by the conjugate of the bottom

Answer 5

okay im working it out give me a sec

Answer 6

\[\large\rm \frac{ 1-i }{ 2+i } \]
example #1
\[\frac{ 1 }{ \sqrt{2}-3 }\]
ex #2
nvm solve freckless example :-)

Answer 7

okay @ freckles first problem is \[\sqrt{2}+3\]

Answer 8

@freckles and the second is \[\frac{ 1 }{ 5 }-\frac{ 3 }{ 5 }i\]

Answer 9

what should be at the denominator ?

Answer 10

first one is not right \[\frac{ 1 }{ \sqrt{2}-3 }\]
use freckles hint:
multiply by conjugate

Answer 11

top part is right

you should multiply both numerator and denominator by conjugate

Answer 12

now I got \[-\frac{ 1 }{ 7 }\]

Answer 13

\[\huge\rm \frac{ 1 }{ \sqrt{2}-3} \times \frac{\sqrt{2}+3}{\sqrt{2}+3}\]
multiply denominator by denominator and numerator by numerator
so 1 times {sqrt{2}+3} = sqrt{2}+3
that should stay at the top
and yes you are right
denominator is -7

Answer 14

so what was ur first step for both questions ??

Answer 15

So the first step would be to conjugate the denominator and then FOIL.. ( am i using the right terms lol)

Answer 16

right first step multiply by conjugate

Answer 17

Okay great I get it now @Nnesha

Answer 18

great

Answer 19

freckles is online you can ask question :-)

Answer 20

yeah my internet has been wacky lately

Answer 21

Hey @freckles so as i write my paragraph to explain how they are similar im first going to state how you have to conjugate the denominator. Then you multiply across for both numerator and denominator would that be considered the foil method or am i using the wrong term?

Answer 22

I would just call it multiplying stead of foil.

For something of the forms:
\[\frac{c+d}{\sqrt{s}+\sqrt{t}} \text{ and } \frac{c+di}{s+ti}\]
to simplify you need to first identify the conjugate of the denominator
once you have identify the conjugate of the denominators, you will take that conjugate and just multiply your fraction on both top and bottom by that conjugate.

Answer 23

I don't like foil method :p
though most people say to multiply something in the form (a+b)(c+d)
you can do that by foil
so it wouldn't be totally wrong to say it, it just isn't very mathematical to say
but I'm sure your teacher would be pleased either way
since you know I think the point of the exercise is for you to understand and for you to come up with your own explanation so I think your explanation would be acceptable

Answer 24

lol okay

Answer 25

i guess you can say foil it bec \[\frac{ c+d }{ \sqrt{s}+\sqrt{d} } \times \frac{\sqrt{s}-\sqrt{t} }{ \sqrt{s}-\sqrt{t} }\]
if you write it as one fraction u r using foil method