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## Homework Statement

Dear Mentors and Helpers,

here's the question:

Find the range of validity for (1 + 3x/2)^(-1) and (1 + 1/(3x))^(-1).

## Homework Equations

## The Attempt at a Solution

For the first binomial series:

-1 < 3x/2 < 1

-2 < 3x < 2 (multiply 2 throughout)

-2/3 < x < 2/3 (divide by 3 throughout)

For the second binomial series:

-1 < 1/(3x) < 1

-3x < 1 < 3x (multiply 3x throughout)

-3x < 1 or 1 < 3x

x > -1/3 (divide -3, inequality change sign) or 1/3 < x (divdide 3)

Therefore I get: x > -1/3 or x > 1/3

However my range isn't correct for the second binomial series can any Mentors or PF helper guide me and correct my mistakes.

Thank you