Inverse Fourier transform of $ \frac{2+\mathrm{j}Ω}{1+\mathrm{j}Ω}$

Question

What is the inverse Fourier transform of $$\frac{2+\mathrm{j}Ω}{1+\mathrm{j}Ω}\,?$$

Answer 1

Taking Partial fraction and writing $$1+\frac{1}{1+jΩ}$$

Now taking Inverse Fourier Transformation

$$F^{-1}(1+\frac{1}{1+jΩ})$$ $$=F^{-1}(1)+F^{-1}(\frac{1}{1+jΩ})$$

$$=\delta(t) + e^{-t}H(t)$$

$H(t)% $=$ $Unit Step Function

$\delta(t)$ = Dirac delta function

Link for the help of inverse of 2nd part.