Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x2−2x4x2−2x−6
Evaluate
(3x2(2x−3))÷((x−2)x2)−((x(2x−3))÷x2)
Multiply the terms
3x2(2x−3)÷((x−2)x2)−((x(2x−3))÷x2)
Multiply the terms
3x2(2x−3)÷x2(x−2)−((x(2x−3))÷x2)
Multiply the terms
3x2(2x−3)÷x2(x−2)−(x(2x−3)÷x2)
Divide the terms
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Evaluate
x(2x−3)÷x2
Rewrite the expression
x2x(2x−3)
Reduce the fraction
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Calculate
x2x
Use the product rule aman=an−m to simplify the expression
x2−11
Subtract the terms
x11
Simplify
x1
x2x−3
3x2(2x−3)÷x2(x−2)−x2x−3
Divide the terms
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Evaluate
3x2(2x−3)÷x2(x−2)
Rewrite the expression
x2(x−2)3x2(2x−3)
Reduce the fraction
x−23(2x−3)
x−23(2x−3)−x2x−3
Reduce fractions to a common denominator
(x−2)x3(2x−3)x−x(x−2)(2x−3)(x−2)
Rewrite the expression
(x−2)x3(2x−3)x−(x−2)x(2x−3)(x−2)
Write all numerators above the common denominator
(x−2)x3(2x−3)x−(2x−3)(x−2)
Multiply the terms
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Evaluate
3(2x−3)x
Multiply the terms
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Evaluate
3(2x−3)
Apply the distributive property
3×2x−3×3
Multiply the numbers
6x−3×3
Multiply the numbers
6x−9
(6x−9)x
Apply the distributive property
6x×x−9x
Multiply the terms
6x2−9x
(x−2)x6x2−9x−(2x−3)(x−2)
Multiply the terms
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Evaluate
(2x−3)(x−2)
Apply the distributive property
2x×x−2x×2−3x−(−3×2)
Multiply the terms
2x2−2x×2−3x−(−3×2)
Multiply the numbers
2x2−4x−3x−(−3×2)
Multiply the numbers
2x2−4x−3x−(−6)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2x2−4x−3x+6
Subtract the terms
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Evaluate
−4x−3x
Collect like terms by calculating the sum or difference of their coefficients
(−4−3)x
Subtract the numbers
−7x
2x2−7x+6
(x−2)x6x2−9x−(2x2−7x+6)
Subtract the terms
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Evaluate
6x2−9x−(2x2−7x+6)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
6x2−9x−2x2+7x−6
Subtract the terms
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Evaluate
6x2−2x2
Collect like terms by calculating the sum or difference of their coefficients
(6−2)x2
Subtract the numbers
4x2
4x2−9x+7x−6
Add the terms
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Evaluate
−9x+7x
Collect like terms by calculating the sum or difference of their coefficients
(−9+7)x
Add the numbers
−2x
4x2−2x−6
(x−2)x4x2−2x−6
Solution
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Evaluate
(x−2)x
Apply the distributive property
x×x−2x
Multiply the terms
x2−2x
x2−2x4x2−2x−6
Show Solution
Find the excluded values
x=0,x=2
Evaluate
((3x2)(2x−3))÷((x−2)(x2))−((x(2x−3))÷(x2))
To find the excluded values,set the denominators equal to 0
(x−2)(x2)=0x2=0
Solve the equations
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Evaluate
(x−2)x2=0
Multiply the terms
x2(x−2)=0
Separate the equation into 2 possible cases
x2=0x−2=0
The only way a power can be 0 is when the base equals 0
x=0x−2=0
Solve the equation
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Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=0x=2
x=0x=2x2=0
The only way a power can be 0 is when the base equals 0
x=0x=2x=0
Solution
x=0,x=2
Show Solution
Find the roots
x1=−1,x2=23
Alternative Form
x1=−1,x2=1.5
Evaluate
((3x2)(2x−3))÷((x−2)(x2))−((x(2x−3))÷(x2))
To find the roots of the expression,set the expression equal to 0
((3x2)(2x−3))÷((x−2)(x2))−((x(2x−3))÷(x2))=0
Find the domain
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Evaluate
{(x−2)(x2)=0x2=0
Calculate
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Evaluate
(x−2)x2=0
Multiply the terms
x2(x−2)=0
Apply the zero product property
{x2=0x−2=0
The only way a power can not be 0 is when the base not equals 0
{x=0x−2=0
Solve the inequality
{x=0x=2
Find the intersection
x∈(−∞,0)∪(0,2)∪(2,+∞)
{x∈(−∞,0)∪(0,2)∪(2,+∞)x2=0
The only way a power can not be 0 is when the base not equals 0
{x∈(−∞,0)∪(0,2)∪(2,+∞)x=0
Find the intersection
x∈(−∞,0)∪(0,2)∪(2,+∞)
((3x2)(2x−3))÷((x−2)(x2))−((x(2x−3))÷(x2))=0,x∈(−∞,0)∪(0,2)∪(2,+∞)
Calculate
((3x2)(2x−3))÷((x−2)(x2))−((x(2x−3))÷(x2))=0
Multiply the terms
(3x2(2x−3))÷((x−2)(x2))−((x(2x−3))÷(x2))=0
Multiply the terms
3x2(2x−3)÷((x−2)(x2))−((x(2x−3))÷(x2))=0
Calculate
3x2(2x−3)÷((x−2)x2)−((x(2x−3))÷(x2))=0
Multiply the terms
3x2(2x−3)÷x2(x−2)−((x(2x−3))÷(x2))=0
Multiply the terms
3x2(2x−3)÷x2(x−2)−(x(2x−3)÷(x2))=0
Calculate
3x2(2x−3)÷x2(x−2)−(x(2x−3)÷x2)=0
Divide the terms
More Steps
Evaluate
x(2x−3)÷x2
Rewrite the expression
x2x(2x−3)
Reduce the fraction
More Steps
Calculate
x2x
Use the product rule aman=an−m to simplify the expression
x2−11
Subtract the terms
x11
Simplify
x1
x2x−3
3x2(2x−3)÷x2(x−2)−x2x−3=0
Divide the terms
More Steps
Evaluate
3x2(2x−3)÷x2(x−2)
Rewrite the expression
x2(x−2)3x2(2x−3)
Reduce the fraction
x−23(2x−3)
x−23(2x−3)−x2x−3=0
Subtract the terms
More Steps
Simplify
x−23(2x−3)−x2x−3
Reduce fractions to a common denominator
(x−2)x3(2x−3)x−x(x−2)(2x−3)(x−2)
Rewrite the expression
(x−2)x3(2x−3)x−(x−2)x(2x−3)(x−2)
Write all numerators above the common denominator
(x−2)x3(2x−3)x−(2x−3)(x−2)
Multiply the terms
More Steps
Evaluate
3(2x−3)x
Multiply the terms
(6x−9)x
Apply the distributive property
6x×x−9x
Multiply the terms
6x2−9x
(x−2)x6x2−9x−(2x−3)(x−2)
Multiply the terms
More Steps
Evaluate
(2x−3)(x−2)
Apply the distributive property
2x×x−2x×2−3x−(−3×2)
Multiply the terms
2x2−2x×2−3x−(−3×2)
Multiply the numbers
2x2−4x−3x−(−3×2)
Multiply the numbers
2x2−4x−3x−(−6)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2x2−4x−3x+6
Subtract the terms
2x2−7x+6
(x−2)x6x2−9x−(2x2−7x+6)
Subtract the terms
More Steps
Evaluate
6x2−9x−(2x2−7x+6)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
6x2−9x−2x2+7x−6
Subtract the terms
4x2−9x+7x−6
Add the terms
4x2−2x−6
(x−2)x4x2−2x−6
(x−2)x4x2−2x−6=0
Cross multiply
4x2−2x−6=(x−2)x×0
Simplify the equation
4x2−2x−6=0
Factor the expression
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Evaluate
4x2−2x−6
Rewrite the expression
2×2x2−2x−2×3
Factor out 2 from the expression
2(2x2−x−3)
Factor the expression
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Evaluate
2x2−x−3
Rewrite the expression
2x2+(−3+2)x−3
Calculate
2x2−3x+2x−3
Rewrite the expression
x×2x−x×3+2x−3
Factor out x from the expression
x(2x−3)+2x−3
Factor out 2x−3 from the expression
(x+1)(2x−3)
2(x+1)(2x−3)
2(x+1)(2x−3)=0
Divide the terms
(x+1)(2x−3)=0
When the product of factors equals 0,at least one factor is 0
x+1=02x−3=0
Solve the equation for x
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Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0−1
Removing 0 doesn't change the value,so remove it from the expression
x=−1
x=−12x−3=0
Solve the equation for x
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Evaluate
2x−3=0
Move the constant to the right-hand side and change its sign
2x=0+3
Removing 0 doesn't change the value,so remove it from the expression
2x=3
Divide both sides
22x=23
Divide the numbers
x=23
x=−1x=23
Check if the solution is in the defined range
x=−1x=23,x∈(−∞,0)∪(0,2)∪(2,+∞)
Find the intersection of the solution and the defined range
x=−1x=23
Solution
x1=−1,x2=23
Alternative Form
x1=−1,x2=1.5
Show Solution