Solve the nonlinear inequality that has the variable in the denominator. 2/x+3=<1/x-3

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We have to solve 2/x+3=<1/x-3

2/(x+3)=<1/(x-3)

=> 2/(x+3) - 1/(x-3) =< 0

=> [2(x-3) - (x+3)]/(x - 3)(x + 3) =< 0

=> (2x - 6 - x-3)/(x - 3)(x + 3) =< 0

=> (x-9)/(x - 3)(x + 3) =< 0

This is less than or equal to 0 if one of the...

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giorgiana1976 | Student

First, we'll move the fraction 1/(x-3) to the left side:

2/(x+3) - 1/(x-3) =< 0

We'll determine the least common denominator:

LCD = (x - 3)(x + 3)

We'll multiply the fractions by LCD:

[2(x-3) - (x+3)]/(x - 3)(x + 3) =< 0

We'll remove the brackets:

(2x - 6 - x-3)/(x - 3)(x + 3) =< 0

(x-9)/(x - 3)(x + 3) =< 0

The values for x are negative if x<-3 and if x belongs to the range (3 ; 9].

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