Solution
Solution
+2
Interval Notation
Decimal Notation
Solution steps
Use the following identity: Therefore
Simplify
Expand
Expand
Apply the distributive law:
Apply minus-plus rules
Multiply the numbers:
Subtract the numbers:
Let:
Factor
Factor
Rewrite as
Rewrite as
Apply radical rule:
Apply exponent rule:
Apply Difference of Two Squares Formula:
Identify the intervals
Find the signs of the factors of
Find the signs of
Move to the right side
Subtract from both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Move to the right side
Subtract from both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Move to the right side
Subtract from both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Find the signs of
Move to the right side
Add to both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Move to the right side
Add to both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Move to the right side
Add to both sides
Simplify
Divide both sides by
Divide both sides by
Simplify
Find the signs of
Find singularity points
Find the zeros of the denominator
Summarize in a table:
Identify the intervals that satisfy the required condition:
Substitute back
If then
Switch sides
For , if then
Simplify
Use the following trivial identity:
Simplify
Use the following trivial identity:
For , if then
Simplify
Use the following trivial identity:
Simplify
Use the following trivial identity:
Simplify
Convert element to fraction:
Since the denominators are equal, combine the fractions:
Multiply the numbers:
Add similar elements:
Combine the intervals
Merge Overlapping Intervals
For , if then
Simplify
Use the following trivial identity:
Simplify
Use the following trivial identity:
Combine the intervals
Merge Overlapping Intervals