Linear Algebra Examples

Find the Domain (-14x)/(6x^2-x^2-2)
Step 1
Set the denominator in equal to to find where the expression is undefined.
Step 2
Solve for .
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Step 2.1
Subtract from .
Step 2.2
Add to both sides of the equation.
Step 2.3
Divide each term in by and simplify.
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Step 2.3.1
Divide each term in by .
Step 2.3.2
Simplify the left side.
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Step 2.3.2.1
Cancel the common factor of .
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Step 2.3.2.1.1
Cancel the common factor.
Step 2.3.2.1.2
Divide by .
Step 2.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.5
Simplify .
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Step 2.5.1
Rewrite as .
Step 2.5.2
Multiply by .
Step 2.5.3
Combine and simplify the denominator.
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Step 2.5.3.1
Multiply by .
Step 2.5.3.2
Raise to the power of .
Step 2.5.3.3
Raise to the power of .
Step 2.5.3.4
Use the power rule to combine exponents.
Step 2.5.3.5
Add and .
Step 2.5.3.6
Rewrite as .
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Step 2.5.3.6.1
Use to rewrite as .
Step 2.5.3.6.2
Apply the power rule and multiply exponents, .
Step 2.5.3.6.3
Combine and .
Step 2.5.3.6.4
Cancel the common factor of .
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Step 2.5.3.6.4.1
Cancel the common factor.
Step 2.5.3.6.4.2
Rewrite the expression.
Step 2.5.3.6.5
Evaluate the exponent.
Step 2.5.4
Simplify the numerator.
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Step 2.5.4.1
Combine using the product rule for radicals.
Step 2.5.4.2
Multiply by .
Step 2.6
The complete solution is the result of both the positive and negative portions of the solution.
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Step 2.6.1
First, use the positive value of the to find the first solution.
Step 2.6.2
Next, use the negative value of the to find the second solution.
Step 2.6.3
The complete solution is the result of both the positive and negative portions of the solution.
Step 3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 4