How to write $5 \over 2-i$ in standard form I am having problems with writing the problem $5 \over 2-i$ in standard form and my book doesn't really show how to do a problem like this with only a number and letter on the bottom.
Take the denominator and flip the sign of the $i$.

$$2-i\implies2+i$$

Now, multiply by $1$.

$$\frac5{2-i}=\frac5{2-i}\color{#034da3}{\underline{\times1}}$$

Any number divided by itself?

$$\color{#034da3}{1=\frac{2+i}{2+i}}$$

$$\frac5{2-i}=\frac5{2-i}\color{#034da3}{\underline{\times\frac{2+i}{2+i}}}$$

$$\text{Numerator}=5\times(2+i)\\\ \\\text{Denominator}=\underbrace{(2-i)(2+i)=4-i^2=5}_{\large\text{Foil, then remember that $i^2=-1$}}$$

$$\frac5{2-i}=\frac{\text{Numerator}}{\text{Denominator}}=\frac{5\times(2+i)}5=2+i$$
hint - multiply the expression with $$\frac{2+i}{2+i}$$