Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
3x9−10x6−6x8+20x55x+15
Evaluate
(5(x2−9))÷((x−2)x5)÷(x−3)÷(x2×3x−10)
Multiply the terms
5(x2−9)÷((x−2)x5)÷(x−3)÷(x2×3x−10)
Multiply the terms
5(x2−9)÷x5(x−2)÷(x−3)÷(x2×3x−10)
Multiply
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Multiply the terms
x2×3x
Multiply the terms with the same base by adding their exponents
x2+1×3
Add the numbers
x3×3
Use the commutative property to reorder the terms
3x3
5(x2−9)÷x5(x−2)÷(x−3)÷(3x3−10)
Rewrite the expression
x5(x−2)5(x2−9)÷(x−3)÷(3x3−10)
Divide the terms
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Evaluate
x5(x−2)5(x2−9)÷(x−3)
Multiply by the reciprocal
x5(x−2)5(x2−9)×x−31
Rewrite the expression
x5(x−2)5(x−3)(x+3)×x−31
Cancel out the common factor x−3
x5(x−2)5(x+3)×1
Multiply the terms
x5(x−2)5(x+3)
x5(x−2)5(x+3)÷(3x3−10)
Multiply by the reciprocal
x5(x−2)5(x+3)×3x3−101
Multiply the terms
x5(x−2)(3x3−10)5(x+3)
Multiply the terms
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Evaluate
5(x+3)
Apply the distributive property
5x+5×3
Multiply the numbers
5x+15
x5(x−2)(3x3−10)5x+15
Solution
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Evaluate
x5(x−2)(3x3−10)
Multiply the terms
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Evaluate
x5(x−2)
Apply the distributive property
x5×x−x5×2
Multiply the terms
x6−x5×2
Use the commutative property to reorder the terms
x6−2x5
(x6−2x5)(3x3−10)
Apply the distributive property
x6×3x3−x6×10−2x5×3x3−(−2x5×10)
Multiply the terms
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Evaluate
x6×3x3
Use the commutative property to reorder the terms
3x6×x3
Multiply the terms
3x9
3x9−x6×10−2x5×3x3−(−2x5×10)
Use the commutative property to reorder the terms
3x9−10x6−2x5×3x3−(−2x5×10)
Multiply the terms
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Evaluate
−2x5×3x3
Multiply the numbers
−6x5×x3
Multiply the terms
−6x8
3x9−10x6−6x8−(−2x5×10)
Multiply the numbers
3x9−10x6−6x8−(−20x5)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x9−10x6−6x8+20x5
3x9−10x6−6x8+20x55x+15
Show Solution
Find the excluded values
x=0,x=2,x=3,x=3390
Evaluate
(5(x2−9))÷((x−2)(x5))÷(x−3)÷(x2×3x−10)
To find the excluded values,set the denominators equal to 0
(x−2)(x5)=0x−3=0x2×3x−10=0
Solve the equations
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Evaluate
(x−2)x5=0
Multiply the terms
x5(x−2)=0
Separate the equation into 2 possible cases
x5=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=2x−3=0x2×3x−10=0
Solve the equations
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Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=0x=2x=3x2×3x−10=0
Solve the equations
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Evaluate
x2×3x−10=0
Multiply
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Evaluate
x2×3x
Multiply the terms with the same base by adding their exponents
x2+1×3
Add the numbers
x3×3
Use the commutative property to reorder the terms
3x3
3x3−10=0
Move the constant to the right-hand side and change its sign
3x3=0+10
Removing 0 doesn't change the value,so remove it from the expression
3x3=10
Divide both sides
33x3=310
Divide the numbers
x3=310
Take the 3-th root on both sides of the equation
3x3=3310
Calculate
x=3310
Simplify the root
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Evaluate
3310
To take a root of a fraction,take the root of the numerator and denominator separately
33310
Multiply by the Conjugate
33×332310×332
Simplify
33×332310×39
Multiply the numbers
33×332390
Multiply the numbers
3390
x=3390
x=0x=2x=3x=3390
Solution
x=0,x=2,x=3,x=3390
Show Solution
Find the roots
x=−3
Evaluate
(5(x2−9))÷((x−2)(x5))÷(x−3)÷(x2×3x−10)
To find the roots of the expression,set the expression equal to 0
(5(x2−9))÷((x−2)(x5))÷(x−3)÷(x2×3x−10)=0
Find the domain
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Evaluate
⎩⎨⎧(x−2)(x5)=0x−3=0x2×3x−10=0
Calculate
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Evaluate
(x−2)x5=0
Multiply the terms
x5(x−2)=0
Apply the zero product property
{x5=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,+∞)x−3=0x2×3x−10=0
Calculate
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Evaluate
x−3=0
Move the constant to the right side
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
⎩⎨⎧x∈(−∞,0)∪(0,2)∪(2,+∞)x=3x2×3x−10=0
Calculate
More Steps
Evaluate
x2×3x−10=0
Multiply
3x3−10=0
Move the constant to the right side
3x3=10
Divide both sides
33x3=310
Divide the numbers
x3=310
Take the 3-th root on both sides of the equation
3x3=3310
Calculate
x=3310
Simplify the root
x=3390
⎩⎨⎧x∈(−∞,0)∪(0,2)∪(2,+∞)x=3x=3390
Find the intersection
x∈(−∞,0)∪(0,3390)∪(3390,2)∪(2,3)∪(3,+∞)
(5(x2−9))÷((x−2)(x5))÷(x−3)÷(x2×3x−10)=0,x∈(−∞,0)∪(0,3390)∪(3390,2)∪(2,3)∪(3,+∞)
Calculate
(5(x2−9))÷((x−2)(x5))÷(x−3)÷(x2×3x−10)=0
Multiply the terms
5(x2−9)÷((x−2)(x5))÷(x−3)÷(x2×3x−10)=0
Calculate
5(x2−9)÷((x−2)x5)÷(x−3)÷(x2×3x−10)=0
Multiply the terms
5(x2−9)÷x5(x−2)÷(x−3)÷(x2×3x−10)=0
Multiply
More Steps
Multiply the terms
x2×3x
Multiply the terms with the same base by adding their exponents
x2+1×3
Add the numbers
x3×3
Use the commutative property to reorder the terms
3x3
5(x2−9)÷x5(x−2)÷(x−3)÷(3x3−10)=0
Rewrite the expression
x5(x−2)5(x2−9)÷(x−3)÷(3x3−10)=0
Divide the terms
More Steps
Evaluate
x5(x−2)5(x2−9)÷(x−3)
Multiply by the reciprocal
x5(x−2)5(x2−9)×x−31
Rewrite the expression
x5(x−2)5(x−3)(x+3)×x−31
Cancel out the common factor x−3
x5(x−2)5(x+3)×1
Multiply the terms
x5(x−2)5(x+3)
x5(x−2)5(x+3)÷(3x3−10)=0
Divide the terms
More Steps
Evaluate
x5(x−2)5(x+3)÷(3x3−10)
Multiply by the reciprocal
x5(x−2)5(x+3)×3x3−101
Multiply the terms
x5(x−2)(3x3−10)5(x+3)
x5(x−2)(3x3−10)5(x+3)=0
Cross multiply
5(x+3)=x5(x−2)(3x3−10)×0
Simplify the equation
5(x+3)=0
Rewrite the expression
x+3=0
Move the constant to the right side
x=0−3
Removing 0 doesn't change the value,so remove it from the expression
x=−3
Check if the solution is in the defined range
x=−3,x∈(−∞,0)∪(0,3390)∪(3390,2)∪(2,3)∪(3,+∞)
Solution
x=−3
Show Solution