Question
Simplify the expression
x3−3x23
Evaluate
(x−33)(x3x)
Remove the unnecessary parentheses
x−33×(x3x)
Divide the terms
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Evaluate
x3x
Use the product rule aman=an−m to simplify the expression
x3−11
Reduce the fraction
x21
x−33×x21
Multiply the terms
(x−3)x23
Multiply the terms
x2(x−3)3
Solution
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Evaluate
x2(x−3)
Apply the distributive property
x2×x−x2×3
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−x2×3
Use the commutative property to reorder the terms
x3−3x2
x3−3x23
Show Solution

Find the excluded values
x=3,x=0
Evaluate
(x−33)(x3x)
To find the excluded values,set the denominators equal to 0
x−3=0x3=0
Solve the equations
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Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x3=0
The only way a power can be 0 is when the base equals 0
x=3x=0
Solution
x=3,x=0
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Find the roots
x∈∅
Evaluate
(x−33)(x3x)
To find the roots of the expression,set the expression equal to 0
(x−33)(x3x)=0
Find the domain
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Evaluate
{x−3=0x3=0
Calculate
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Evaluate
x−3=0
Move the constant to the right side
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
{x=3x3=0
The only way a power can not be 0 is when the base not equals 0
{x=3x=0
Find the intersection
x∈(−∞,0)∪(0,3)∪(3,+∞)
(x−33)(x3x)=0,x∈(−∞,0)∪(0,3)∪(3,+∞)
Calculate
(x−33)(x3x)=0
Remove the unnecessary parentheses
x−33×(x3x)=0
Divide the terms
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Evaluate
x3x
Use the product rule aman=an−m to simplify the expression
x3−11
Reduce the fraction
x21
x−33×x21=0
Multiply the terms
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Multiply the terms
x−33×x21
Multiply the terms
(x−3)x23
Multiply the terms
x2(x−3)3
x2(x−3)3=0
Cross multiply
3=x2(x−3)×0
Simplify the equation
3=0
Solution
x∈∅
Show Solution
