Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
x∈(−∞,0)∪(1,+∞)
Evaluate
x1<1
Find the domain
x1<1,x=0
Move the expression to the left side
x1−1<0
Subtract the terms
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Evaluate
x1−1
Reduce fractions to a common denominator
x1−xx
Write all numerators above the common denominator
x1−x
x1−x<0
Set the numerator and denominator of x1−x equal to 0 to find the values of x where sign changes may occur
1−x=0x=0
Calculate
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Evaluate
1−x=0
Move the constant to the right-hand side and change its sign
−x=0−1
Removing 0 doesn't change the value,so remove it from the expression
−x=−1
Change the signs on both sides of the equation
x=1
x=1x=0
Determine the test intervals using the critical values
x<00<x<1x>1
Choose a value form each interval
x1=−1x2=21x3=2
To determine if x<0 is the solution to the inequality,test if the chosen value x=−1 satisfies the initial inequality
More Steps

Evaluate
−11<1
Divide the terms
−1<1
Check the inequality
true
x<0 is the solutionx2=21x3=2
To determine if 0<x<1 is the solution to the inequality,test if the chosen value x=21 satisfies the initial inequality
More Steps

Evaluate
211<1
Multiply by the reciprocal
2<1
Check the inequality
false
x<0 is the solution0<x<1 is not a solutionx3=2
To determine if x>1 is the solution to the inequality,test if the chosen value x=2 satisfies the initial inequality
More Steps

Evaluate
21<1
Calculate
0.5<1
Check the inequality
true
x<0 is the solution0<x<1 is not a solutionx>1 is the solution
The original inequality is a strict inequality,so does not include the critical value ,the final solution is x∈(−∞,0)∪(1,+∞)
x∈(−∞,0)∪(1,+∞)
Check if the solution is in the defined range
x∈(−∞,0)∪(1,+∞),x=0
Solution
x∈(−∞,0)∪(1,+∞)
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