Algebra Examples

Find Where Undefined/Discontinuous ((2y^3-10y^2-48y)/(3y-24))÷((y^2+5y+6)/(9y^4+18y^3))
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
Add to both sides of the equation.
Step 2.2
Divide each term in by and simplify.
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Step 2.2.1
Divide each term in by .
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
Divide by .
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
Factor out of .
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Step 4.1.1
Factor out of .
Step 4.1.2
Factor out of .
Step 4.1.3
Factor out of .
Step 4.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 4.3
Set equal to and solve for .
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Step 4.3.1
Set equal to .
Step 4.3.2
Solve for .
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Step 4.3.2.1
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 4.3.2.2
Simplify .
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Step 4.3.2.2.1
Rewrite as .
Step 4.3.2.2.2
Pull terms out from under the radical, assuming real numbers.
Step 4.4
Set equal to and solve for .
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Step 4.4.1
Set equal to .
Step 4.4.2
Subtract from both sides of the equation.
Step 4.5
The final solution is all the values that make true.
Step 5
Set the denominator in equal to to find where the expression is undefined.
Step 6
Solve for .
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Step 6.1
Set the numerator equal to zero.
Step 6.2
Solve the equation for .
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Step 6.2.1
Factor using the AC method.
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Step 6.2.1.1
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Step 6.2.1.2
Write the factored form using these integers.
Step 6.2.2
If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .
Step 6.2.3
Set equal to and solve for .
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Step 6.2.3.1
Set equal to .
Step 6.2.3.2
Subtract from both sides of the equation.
Step 6.2.4
Set equal to and solve for .
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Step 6.2.4.1
Set equal to .
Step 6.2.4.2
Subtract from both sides of the equation.
Step 6.2.5
The final solution is all the values that make true.
Step 6.3
Exclude the solutions that do not make true.
Step 7
The equation is undefined where the denominator equals , the argument of a square root is less than , or the argument of a logarithm is less than or equal to .
Step 8