Question
Simplify the expression
2x3x−4xx
Evaluate
x21(2x3−x×2)
Use the commutative property to reorder the terms
x21(2x3−2x)
Subtract the terms
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Simplify
2x3−2x
Reduce fractions to a common denominator
2x3−22x×2
Write all numerators above the common denominator
2x3−2x×2
Multiply the terms
2x3−4x
x21×2x3−4x
Multiply the terms
2x21(x3−4x)
Solution
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Evaluate
x21(x3−4x)
Use anm=nam to transform the expression
x×(x3−4x)
Multiply each term in the parentheses by x
x×x3+x×(−4x)
Calculate the product
x3x+x×(−4x)
Calculate the product
x3x−4xx
2x3x−4xx
Show Solution

Find the roots
x1=0,x2=2
Evaluate
x21(2x3−x1×2)
To find the roots of the expression,set the expression equal to 0
x21(2x3−x1×2)=0
Find the domain
x21(2x3−x1×2)=0,x≥0
Calculate
x21(2x3−x1×2)=0
Evaluate the power
x21(2x3−x×2)=0
Use the commutative property to reorder the terms
x21(2x3−2x)=0
Subtract the terms
More Steps

Simplify
2x3−2x
Reduce fractions to a common denominator
2x3−22x×2
Write all numerators above the common denominator
2x3−2x×2
Multiply the terms
2x3−4x
x21×2x3−4x=0
Multiply the terms
2x21(x3−4x)=0
Simplify
x21(x3−4x)=0
Separate the equation into 2 possible cases
x21=0x3−4x=0
The only way a root could be 0 is when the radicand equals 0
x=0x3−4x=0
Solve the equation
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Evaluate
x3−4x=0
Factor the expression
x(x2−4)=0
Separate the equation into 2 possible cases
x=0x2−4=0
Solve the equation
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Evaluate
x2−4=0
Move the constant to the right-hand side and change its sign
x2=0+4
Removing 0 doesn't change the value,so remove it from the expression
x2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4
Simplify the expression
x=±2
Separate the equation into 2 possible cases
x=2x=−2
x=0x=2x=−2
x=0x=0x=2x=−2
Find the union
x=0x=2x=−2
Check if the solution is in the defined range
x=0x=2x=−2,x≥0
Find the intersection of the solution and the defined range
x=0x=2
Solution
x1=0,x2=2
Show Solution
