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Question

Given the function R(x)=x-6/x+6, find the values of x that make the function less than or equal to zero. Write the solution in interval notation.

Answer 1

In order to get rid of a fraction, always multiply by the denominator.

If you multiply x+6 on both sides, you are left with x -6 less than or equal to zero.

Add 6 on both sides and x is less than or equal to zeero.

However, there is an excluded value x = -6 because if x = -6 you get zero and the denominator and you cannot divided by 0.

So (-inf,-6) U (-6, 6] U [6, inf)