Math Problem Statement
2/x+1 > x-1/x+1
Solution
To solve the inequality
let's follow these steps:
Step 1: Combine like terms
We can rewrite the inequality as:
Since the right-hand side already has a common denominator , we can subtract the fractions:
Step 2: Simplify the expression
Combine the fractions:
Now, expand and simplify the numerator:
So the inequality becomes:
Step 3: Factor the numerator
The expression in the numerator can be factored:
We can factor the quadratic as:
So, the inequality is:
Step 4: Analyze the sign changes
We need to determine the intervals where the expression is positive. The critical points occur where the numerator or denominator is zero:
We will now test the intervals determined by these points:
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Math Problem Analysis
Mathematical Concepts
Inequalities
Rational Functions
Quadratic Equations
Formulas
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Theorems
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Suitable Grade Level
Grades 10-12