Evaluate
\text{Indeterminate}
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\frac{15\left(2-\sqrt{-1}\right)}{\left(2+\sqrt{-1}\right)\left(2-\sqrt{-1}\right)}
Rationalize the denominator of \frac{15}{2+\sqrt{-1}} by multiplying numerator and denominator by 2-\sqrt{-1}.
\frac{15\left(2-\sqrt{-1}\right)}{2^{2}-\left(\sqrt{-1}\right)^{2}}
Consider \left(2+\sqrt{-1}\right)\left(2-\sqrt{-1}\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.
\frac{15\left(2-\sqrt{-1}\right)}{4+1}
Square 2. Square \sqrt{-1}.
\frac{15\left(2-\sqrt{-1}\right)}{5}
Subtract -1 from 4 to get 5.
3\left(2-\sqrt{-1}\right)
Divide 15\left(2-\sqrt{-1}\right) by 5 to get 3\left(2-\sqrt{-1}\right).
6-3\sqrt{-1}
Use the distributive property to multiply 3 by 2-\sqrt{-1}.
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