Question

Please explain how I can simplify this: (1/x) / (1/x)^2 + 1 to get this answer x/ x^2 + 1

Answer 1

Answer:

see explanation

Step-by-step explanation:

Given

$\frac{\frac{1}{x} }{(\frac{1}{x})^2+1 }$

= $\frac{\frac{1}{x} }{\frac{1}{x^2}+1 }$

Multiply numerator/ denominator by x² to clear the fractions

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

= $\frac{x}{1+x^2}$

= $\frac{x}{x^2+1}$