Question

Combine 4/i - 6/(8-i)

Answer 1

Problem looks like this : \[\frac{ 4 }{ i } - \frac{ 6 }{ 8-i }\] I know that (8+i) is the conjugate of (8-i) and that the top and bottom of the second fraction has to multiplied by that. I'm not sure what to do with the first fraction, though. Help would be appreciated.

Answer 2

multiply by i to both numerator and denominator

Answer 3

1/i = -i

Answer 4

does it make sense?

Answer 5

None of my answer have 8 as a denominator, so that isn't correct. :(

Answer 6

*the answers

Answer 7

\[[\frac{ 4 }{ i }*\frac{ i }{ i }]-[\frac{ 6 }{ 8-i }*\frac{ 8+i }{ 8+i } ]\] you are done

Answer 8

@MoonlitFate can you do the rest?

Answer 9

I thought that both denominators had to be equal to each other to combine them. Similar to just normal fractions. All of the available answers have equal denominators...

Answer 10

no , you have to rationalise first

Answer 11

even if you'll do that , things will become more complex

Answer 12

Hm. So to answer the first part of the equation the answer would be: \[\frac{ 4i }{ i ^{2} } - \frac{ 48 + 6i }{ 65}\]

Answer 13

i guess it is correct

Answer 14

\[i^2= -1\]

Answer 15

\[-4i +\frac{ 48+6i }{ 65 }\] now it's just simple math

Answer 16

Oh. Multiply the first term by 65 and just add. Got it. So the answer would be: \[\frac{ -48 }{ 65 } - \frac{ -266i }{ 65 }\]

Answer 17

wait a sec

Answer 18

i am sorry...you are absolutely right :)

Answer 19

Ah, haha. I guess what confused me was one of the first steps. Why you had to multiply the first term by i^2