Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
6x266x−6x×x
Evaluate
x−611−x−65×61
Use the commutative property to reorder the terms
x−611−61x−65
Express with a positive exponent using a−n=an1
x6111−61x−65
Rewrite the expression
More Steps
Evaluate
−61x−65
Express with a positive exponent using a−n=an1
−61×x651
Rewrite the expression
−6x651
x6111−6x651
Simplify the expression
More Steps
Evaluate
x611
Use anm=nam to transform the expression
6x11
Rewrite the exponent as a sum
6x6+5
Use am+n=am×an to expand the expression
6x6×x5
The root of a product is equal to the product of the roots of each factor
6x6×6x5
Reduce the index of the radical and exponent with 6
x6x5
x6x51−6x651
Use anm=nam to transform the expression
x6x51−66x51
Rationalize the denominator
More Steps
Evaluate
x6x51
Multiply by the Conjugate
x6x5×6x1×6x
Calculate
x×x1×6x
Any expression multiplied by 1 remains the same
x×x6x
Calculate
x26x
x26x−66x51
Rationalize the denominator
More Steps
Evaluate
−66x51
Multiply by the Conjugate
−66x5×6x1×6x
Calculate
−6x1×6x
Any expression multiplied by 1 remains the same
−6x6x
x26x−6x6x
Reduce fractions to a common denominator
x2×66x×6−6x×x6x×x
Use the commutative property to reorder the terms
6x26x×6−6x×x6x×x
Multiply the terms
6x26x×6−6x26x×x
Write all numerators above the common denominator
6x26x×6−6x×x
Solution
6x266x−6x×x
Show Solution
Find the roots
x=6
Evaluate
x−611−x−65(61)
To find the roots of the expression,set the expression equal to 0
x−611−x−65(61)=0
Find the domain
x−611−x−65(61)=0,x>0
Calculate
x−611−x−65(61)=0
Remove the unnecessary parentheses
x−611−x−65×61=0
Use the commutative property to reorder the terms
x−611−61x−65=0
Express with a positive exponent using a−n=an1
x6111−61x−65=0
Rewrite the expression
More Steps
Evaluate
−61x−65
Express with a positive exponent using a−n=an1
−61×x651
Rewrite the expression
−6x651
x6111−6x651=0
Multiply both sides of the equation by LCD
(x6111−6x651)×6x611=0×6x611
Simplify the equation
More Steps
Evaluate
(x6111−6x651)×6x611
Apply the distributive property
x6111×6x611−6x651×6x611
Simplify
1×6−x
Any expression multiplied by 1 remains the same
6−x
6−x=0×6x611
Any expression multiplied by 0 equals 0
6−x=0
Move the constant to the right side
−x=0−6
Removing 0 doesn't change the value,so remove it from the expression
−x=−6
Change the signs on both sides of the equation
x=6
Check if the solution is in the defined range
x=6,x>0
Solution
x=6
Show Solution