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Answer:
Step-by-step explanation:
<u>Inequalities</u>
They relate one or more variables with comparison operators other than the equality.
We must find the set of values for x that make the expression stand
The roots of numerator can be found by trial and error. The only real roots are x=1 and x=-1/2.
The roots of the denominator are easy to find since it's a second-degree polynomial: x=1, x=1/2. Hence, the given expression can be factored as
Simplifying by x-1 and taking x=1 out of the possible solutions:
We need to find the values of x that make the expression less or equal to 0, i.e. negative or zero. The expressions
is always positive and doesn't affect the result. It can be neglected. The expression
can be 0 or positive. We exclude the value x=1/2 from the solution and neglect the expression as being always positive. This leads to analyze the remaining expression
For the expression to be negative, both signs must be opposite, that is
Or
Note we have excluded x=1 from the solution.
The first inequality gives us the solution
The second inequality gives no solution because it's impossible to comply with both conditions.
Thus, the solution for the given inequality is