Answer:
see explanation
Step-by-step explanation:
Given
[tex]\frac{\frac{1}{x} }{(\frac{1}{x})^2+1 }[/tex]
= [tex]\frac{\frac{1}{x} }{\frac{1}{x^2}+1 }[/tex]
Multiply numerator/ denominator by x² to clear the fractions
= [tex]\frac{\frac{1}{x}(x^2) }{(\frac{1}{x^2}+1)x^2 }[/tex]
= [tex]\frac{x}{1+x^2}[/tex]
= [tex]\frac{x}{x^2+1}[/tex]
