Simplifier au maximum les écritures suivantes :

Question

\(A=\frac{e^{2x}}{e^{3x}}\)

Solution

\(A=e^{2x-3x}=e^{-x}\)

Question

\(B=e^x(1+2e^{-x})\)

Solution

\(B=e^x+2e^xe^{-x}=e^2+2\)

Question

\(C=\frac{e^{x+2}}{e^{x+1}}\)

Solution

\(C=e^{x+2-(x+1)}=e\)

Question

\(D=(e^x+e^{-x})^2\)

Solution

\(D=e^{2x}+2e^xe^{-x}+e^{-2x}=e^{2x}+e^{-2x}+2\)

Question

\(E=\frac{e^{2x-1}}{e^{2x}}\)

Solution

\(E=e^{2x-1-2x}=e^{-1}\)

Question

\(F=\frac{e^{3x}+e^x}{e^{2x}+1}\)

Solution

\(F=\frac{e^x(e^{2x}+1)}{e^{2x}+1}=e^x\)