Question

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

Answer 1

see explanation

Explanation:

Given

`((1)/(x) )/(((1)/(x))^2+1 )`

=
`((1)/(x) )/((1)/(x^2)+1 )`

Multiply numerator/ denominator by x² to clear the fractions

=
`((1)/(x)(x^2) )/(((1)/(x^2)+1)x^2 )`

=
`(x)/(1+x^2)`

=
`(x)/(x^2+1)`