Question

simplify the expression.
-6+i\-5+i

Answer 1

use the conjugate of the denominator, to "simplify" or "rationalize" the denominator, thus getting rid of that pesky "i"
so the denominator is -5+i it's conjugate is the same thing but with a negative in between, that is -5 - i

so \(\bf \cfrac{ -6+i }{ -5+i }\times \cfrac{-5-i}{-5-i}\implies \cfrac{(-6+i)(-5-i)}{(-5+i)(-5-i)}\\ \quad \\
\textit{keeping in mind that }\qquad (a-b)(a+b) = a^2-b^2\qquad then\\ \quad \\
\cfrac{(-6+i)(-5-i)}{(-5+i)(-5-i)}\implies \cfrac{(-6+i)(-5-i)}{-5^2-i^2}
\)

multiply and add like-terms, see what you get