Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
2x32−x2
Evaluate
xx21−21
Subtract the terms
More Steps
Simplify
x21−21
Reduce fractions to a common denominator
x2×22−2x2x2
Use the commutative property to reorder the terms
2x22−2x2x2
Write all numerators above the common denominator
2x22−x2
x2x22−x2
Multiply by the reciprocal
2x22−x2×x1
Multiply the terms
2x2×x2−x2
Solution
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
2x32−x2
Show Solution
Find the excluded values
x=0
Evaluate
xx21−21
To find the excluded values,set the denominators equal to 0
x2=0x=0
The only way a power can be 0 is when the base equals 0
x=0x=0
Solution
x=0
Show Solution
Find the roots
x1=−2,x2=2
Alternative Form
x1≈−1.414214,x2≈1.414214
Evaluate
xx21−21
To find the roots of the expression,set the expression equal to 0
xx21−21=0
Find the domain
More Steps
Evaluate
{x2=0x=0
The only way a power can not be 0 is when the base not equals 0
{x=0x=0
Find the intersection
x=0
xx21−21=0,x=0
Calculate
xx21−21=0
Subtract the terms
More Steps
Simplify
x21−21
Reduce fractions to a common denominator
x2×22−2x2x2
Use the commutative property to reorder the terms
2x22−2x2x2
Write all numerators above the common denominator
2x22−x2
x2x22−x2=0
Divide the terms
More Steps
Evaluate
x2x22−x2
Multiply by the reciprocal
2x22−x2×x1
Multiply the terms
2x2×x2−x2
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
2x32−x2
2x32−x2=0
Cross multiply
2−x2=2x3×0
Simplify the equation
2−x2=0
Rewrite the expression
−x2=−2
Change the signs on both sides of the equation
x2=2
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±2
Separate the equation into 2 possible cases
x=2x=−2
Check if the solution is in the defined range
x=2x=−2,x=0
Find the intersection of the solution and the defined range
x=2x=−2
Solution
x1=−2,x2=2
Alternative Form
x1≈−1.414214,x2≈1.414214
Show Solution