Question
Simplify the expression
−2x36x2+10+5x
Evaluate
(2x×21x−114−4x2−2x−21x×1)÷(x2×22x×1)
Divide the terms
(2x×21x−114−4x2−2x−21x×1)÷(x2×1×x×1)
Divide the terms
(2x×21x−14−4x2−2x−21x×1)÷(x2×1×x×1)
Covert the mixed number to an improper fraction
More Steps

Convert the expressions
14
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
11+4
Add the terms
5
(2x×21x−5−4x2−2x−21x×1)÷(x2×1×x×1)
Multiply
More Steps

Multiply the terms
2x×21x
Multiply the terms
More Steps

Evaluate
2×21
Reduce the fraction
1×1
Any expression multiplied by 1 remains the same
1
x×x
Multiply the terms
x2
(x2−5−4x2−2x−21x×1)÷(x2×1×x×1)
Multiply the terms
(x2−5−4x2−2x−21x)÷(x2×1×x×1)
Subtract the terms
More Steps

Evaluate
x2−5−4x2−2x−21x
Subtract the terms
More Steps

Evaluate
x2−4x2
Collect like terms by calculating the sum or difference of their coefficients
(1−4)x2
Subtract the numbers
−3x2
−3x2−5−2x−21x
Subtract the terms
More Steps

Evaluate
−2x−21x
Collect like terms by calculating the sum or difference of their coefficients
(−2−21)x
Subtract the numbers
−25x
−3x2−5−25x
(−3x2−5−25x)÷(x2×1×x×1)
Multiply the terms
More Steps

Multiply the terms
x2×1×x×1
Rewrite the expression
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
(−3x2−5−25x)÷x3
Rewrite the expression
More Steps

Evaluate
−3x2−5−25x
Rewrite the expression
−3x2−5−25x
Reduce fractions to a common denominator
−23x2×2−25×2−25x
Write all numerators above the common denominator
2−3x2×2−5×2−5x
Multiply the terms
2−6x2−5×2−5x
Multiply the numbers
2−6x2−10−5x
Use b−a=−ba=−ba to rewrite the fraction
−26x2+10+5x
(−26x2+10+5x)÷x3
Multiply by the reciprocal
−26x2+10+5x×x31
Solution
−2x36x2+10+5x
Show Solution

Find the excluded values
x=0
Evaluate
(2x×21x−114−4x2−2x−21x×1)÷(x2×22x×1)
To find the excluded values,set the denominators equal to 0
x2×22x×1=0
Simplify
More Steps

Evaluate
x2×22x×1
Divide the terms
x2×1×x×1
Rewrite the expression
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3=0
Solution
x=0
Show Solution

Find the roots
x∈/R
Evaluate
(2x×21x−114−4x2−2x−21x×1)÷(x2×22x×1)
To find the roots of the expression,set the expression equal to 0
(2x×21x−114−4x2−2x−21x×1)÷(x2×22x×1)=0
Find the domain
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Evaluate
x2×22x×1=0
Simplify
More Steps

Evaluate
x2×22x×1
Divide the terms
x2×1×x×1
Rewrite the expression
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3=0
The only way a power can not be 0 is when the base not equals 0
x=0
(2x×21x−114−4x2−2x−21x×1)÷(x2×22x×1)=0,x=0
Calculate
(2x×21x−114−4x2−2x−21x×1)÷(x2×22x×1)=0
Divide the terms
(2x×21x−14−4x2−2x−21x×1)÷(x2×22x×1)=0
Covert the mixed number to an improper fraction
More Steps

Convert the expressions
14
Multiply the denominator of the fraction by the whole number and add the numerator of the fraction
11+4
Add the terms
5
(2x×21x−5−4x2−2x−21x×1)÷(x2×22x×1)=0
Multiply
More Steps

Multiply the terms
2x×21x
Multiply the terms
More Steps

Evaluate
2×21
Reduce the fraction
1×1
Any expression multiplied by 1 remains the same
1
x×x
Multiply the terms
x2
(x2−5−4x2−2x−21x×1)÷(x2×22x×1)=0
Subtract the terms
More Steps

Simplify
x2−5−4x2
Subtract the terms
More Steps

Evaluate
x2−4x2
Collect like terms by calculating the sum or difference of their coefficients
(1−4)x2
Subtract the numbers
−3x2
−3x2−5
(−3x2−5−2x−21x×1)÷(x2×22x×1)=0
Multiply the terms
(−3x2−5−2x−21x)÷(x2×22x×1)=0
Subtract the terms
More Steps

Simplify
−3x2−5−2x−21x
Subtract the terms
More Steps

Evaluate
−2x−21x
Collect like terms by calculating the sum or difference of their coefficients
(−2−21)x
Subtract the numbers
−25x
−3x2−5−25x
(−3x2−5−25x)÷(x2×22x×1)=0
Divide the terms
More Steps

Evaluate
22
Reduce the numbers
11
Calculate
1
(−3x2−5−25x)÷(x2×1×x×1)=0
Multiply the terms
More Steps

Multiply the terms
x2×1×x×1
Rewrite the expression
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
(−3x2−5−25x)÷x3=0
Divide the terms
More Steps

Evaluate
(−3x2−5−25x)÷x3
Rewrite the expression
More Steps

Evaluate
−3x2−5−25x
Rewrite the expression
−3x2−5−25x
Reduce fractions to a common denominator
−23x2×2−25×2−25x
Write all numerators above the common denominator
2−3x2×2−5×2−5x
Multiply the terms
2−6x2−5×2−5x
Multiply the numbers
2−6x2−10−5x
Use b−a=−ba=−ba to rewrite the fraction
−26x2+10+5x
(−26x2+10+5x)÷x3
Multiply by the reciprocal
−26x2+10+5x×x31
Multiply the terms
−2x36x2+10+5x
−2x36x2+10+5x=0
Rewrite the expression
2x3−6x2−10−5x=0
Cross multiply
−6x2−10−5x=2x3×0
Simplify the equation
−6x2−10−5x=0
Rewrite in standard form
−6x2−5x−10=0
Multiply both sides
6x2+5x+10=0
Substitute a=6,b=5 and c=10 into the quadratic formula x=2a−b±b2−4ac
x=2×6−5±52−4×6×10
Simplify the expression
x=12−5±52−4×6×10
Simplify the expression
More Steps

Evaluate
52−4×6×10
Multiply the numbers
More Steps

Multiply the terms
4×6×10
Multiply the terms
24×10
Multiply the numbers
240
52−240
Evaluate the power
25−240
Subtract the numbers
−215
x=12−5±−215
Solution
x∈/R
Show Solution
