SOLUTION: Please help me solve: 6/i - 8/8-i. Combine and write the answer in standard form.

Question 125695: Please help me solve: 6/i - 8/8-i. Combine and write the answer in standard form.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
6/i - 8/8-i. Combine and write the answer in standard form
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[6(8-i)-8i]/[i(8-i)]
= [48-14i]/[8i+1]
Multiply numerator and denominator by (1+8i) to get:
= [2(24-7i)(1-8i)]/(64+1)
= [2(24-56-199i]/65
= (-64+398i)/65
= (-64/65)+ (398/65)i
=========================
Cheers,
Stan H.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
.

The first thing to do is rationalize the denominators, i.e. get the i out of each denominator and then you will be able to find a LCD to allow you to add the fractions.

The first fraction is easy, you just multiply by , giving you (remember )

The other fraction requires you to remember the factorization of the difference of two squares. . Using this, we could multiply the denominator of the second fraction, by its conjugate to obtain , but to do that we also have to multiply the numerator by the same thing. The result is that the second fraction looks like

Putting it all together we get

65 is clearly the LCD, so

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