Finite Math Examples

Find the Domain y=( fourth root of 5-10x)/((x-3)(x+4))
Step 1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 2
Solve for .
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Step 2.1
Subtract from both sides of the inequality.
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
Step 2.2.2
Simplify the left side.
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Step 2.2.2.1
Cancel the common factor of .
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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.
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Step 2.2.3.1
Cancel the common factor of and .
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Step 2.2.3.1.1
Factor out of .
Step 2.2.3.1.2
Cancel the common factors.
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Step 2.2.3.1.2.1
Factor out of .
Step 2.2.3.1.2.2
Cancel the common factor.
Step 2.2.3.1.2.3
Rewrite the expression.
Step 3
Set the denominator in equal to to find where the expression is undefined.
Step 4
Solve for .
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Step 4.1
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.2
Set equal to and solve for .
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Step 4.2.1
Set equal to .
Step 4.2.2
Add to both sides of the equation.
Step 4.3
Set equal to and solve for .
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Step 4.3.1
Set equal to .
Step 4.3.2
Subtract from both sides of the equation.
Step 4.4
The final solution is all the values that make true.
Step 5
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 6