Linear Algebra Examples

Find the Domain y=(t^3+t)/(2t^3+1)
Step 1
Set the denominator in equal to to find where the expression is undefined.
Step 2
Solve for .
Tap for more steps...
Step 2.1
Subtract from both sides of the equation.
Step 2.2
Divide each term in by and simplify.
Tap for more steps...
Step 2.2.1
Divide each term in by .
Step 2.2.2
Simplify the left side.
Tap for more steps...
Step 2.2.2.1
Cancel the common factor of .
Tap for more steps...
Step 2.2.2.1.1
Cancel the common factor.
Step 2.2.2.1.2
Divide by .
Step 2.2.3
Simplify the right side.
Tap for more steps...
Step 2.2.3.1
Move the negative in front of the fraction.
Step 2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.4
Simplify .
Tap for more steps...
Step 2.4.1
Rewrite as .
Tap for more steps...
Step 2.4.1.1
Rewrite as .
Step 2.4.1.2
Rewrite as .
Step 2.4.2
Pull terms out from under the radical.
Step 2.4.3
Raise to the power of .
Step 2.4.4
Rewrite as .
Step 2.4.5
Any root of is .
Step 2.4.6
Multiply by .
Step 2.4.7
Combine and simplify the denominator.
Tap for more steps...
Step 2.4.7.1
Multiply by .
Step 2.4.7.2
Raise to the power of .
Step 2.4.7.3
Use the power rule to combine exponents.
Step 2.4.7.4
Add and .
Step 2.4.7.5
Rewrite as .
Tap for more steps...
Step 2.4.7.5.1
Use to rewrite as .
Step 2.4.7.5.2
Apply the power rule and multiply exponents, .
Step 2.4.7.5.3
Combine and .
Step 2.4.7.5.4
Cancel the common factor of .
Tap for more steps...
Step 2.4.7.5.4.1
Cancel the common factor.
Step 2.4.7.5.4.2
Rewrite the expression.
Step 2.4.7.5.5
Evaluate the exponent.
Step 2.4.8
Simplify the numerator.
Tap for more steps...
Step 2.4.8.1
Rewrite as .
Step 2.4.8.2
Raise to the power of .
Step 3
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 4