Question
Simplify the expression
x−210x4−3
Evaluate
x−25x3×2x−3
Solution
More Steps

Evaluate
5x3×2x
Multiply the terms
10x3×x
Multiply the terms with the same base by adding their exponents
10x3+1
Add the numbers
10x4
x−210x4−3
Show Solution

Find the excluded values
x=2
Evaluate
x−25x3×2x−3
To find the excluded values,set the denominators equal to 0
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Solution
x=2
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Find the roots
x1=−1043000,x2=1043000
Alternative Form
x1≈−0.740083,x2≈0.740083
Evaluate
x−25x3×2x−3
To find the roots of the expression,set the expression equal to 0
x−25x3×2x−3=0
Find the domain
More Steps

Evaluate
x−2=0
Move the constant to the right side
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x−25x3×2x−3=0,x=2
Calculate
x−25x3×2x−3=0
Multiply
More Steps

Multiply the terms
5x3×2x
Multiply the terms
10x3×x
Multiply the terms with the same base by adding their exponents
10x3+1
Add the numbers
10x4
x−210x4−3=0
Cross multiply
10x4−3=(x−2)×0
Simplify the equation
10x4−3=0
Move the constant to the right side
10x4=3
Divide both sides
1010x4=103
Divide the numbers
x4=103
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4103
Simplify the expression
More Steps

Evaluate
4103
To take a root of a fraction,take the root of the numerator and denominator separately
41043
Multiply by the Conjugate
410×410343×4103
Simplify
410×410343×41000
Multiply the numbers
More Steps

Evaluate
43×41000
The product of roots with the same index is equal to the root of the product
43×1000
Calculate the product
43000
410×410343000
Multiply the numbers
More Steps

Evaluate
410×4103
The product of roots with the same index is equal to the root of the product
410×103
Calculate the product
4104
Reduce the index of the radical and exponent with 4
10
1043000
x=±1043000
Separate the equation into 2 possible cases
x=1043000x=−1043000
Check if the solution is in the defined range
x=1043000x=−1043000,x=2
Find the intersection of the solution and the defined range
x=1043000x=−1043000
Solution
x1=−1043000,x2=1043000
Alternative Form
x1≈−0.740083,x2≈0.740083
Show Solution
