Answer
$$\frac{2-i}{2+i}=\frac{3}{5}-\frac{4}{5}i$$
Work Step by Step
$$A=\frac{2-i}{2+i}$$
For fraction operation, we need to multiply the complex conjugate of the denominator in both the numerator and the denominator.
In other words. here we need to multiply both the numerator and denominator by $(2-i)$ $$A=\frac{2-i}{2+i}\frac{2-i}{2-i}$$ $$A=\frac{(2-i)^2}{4-i^2}$$ (for $(a-b)(a+b)=a^2-b^2$) $$A=\frac{4+i^2-4i}{4-(-1)}$$ (for $(a-b)^2=a^2+b^2-2ab$)$$A=\frac{4-1-4i}{4+1}$$ $$A=\frac{3-4i}{5}$$ $$A=\frac{3}{5}-\frac{4}{5}i$$