Question
Simplify the expression
12
Evaluate
(((3sqrt×2)−(2sqrt×3))÷((3sqrt×2)+(2sqrt×3)))+(sqrt×12÷(sqrt×3−sqrt×2))
Multiply the terms
((6sqrt−(2sqrt×3))÷((3sqrt×2)+(2sqrt×3)))+(sqrt×12÷(sqrt×3−sqrt×2))
Multiply the terms
((6sqrt−6sqrt)÷((3sqrt×2)+(2sqrt×3)))+(sqrt×12÷(sqrt×3−sqrt×2))
Subtract the terms
(0÷((3sqrt×2)+(2sqrt×3)))+(sqrt×12÷(sqrt×3−sqrt×2))
Multiply the terms
(0÷(6sqrt+(2sqrt×3)))+(sqrt×12÷(sqrt×3−sqrt×2))
Multiply the terms
(0÷(6sqrt+6sqrt))+(sqrt×12÷(sqrt×3−sqrt×2))
Add the terms
More Steps

Evaluate
6sqrt+6sqrt
Collect like terms by calculating the sum or difference of their coefficients
(6+6)sqrt
Add the numbers
12sqrt
(0÷12sqrt)+(sqrt×12÷(sqrt×3−sqrt×2))
Divide the terms
0+(sqrt×12÷(sqrt×3−sqrt×2))
Use the commutative property to reorder the terms
0+(sqrt×12÷(3sqrt−sqrt×2))
Use the commutative property to reorder the terms
0+(sqrt×12÷(3sqrt−2sqrt))
Subtract the terms
More Steps

Simplify
3sqrt−2sqrt
Collect like terms by calculating the sum or difference of their coefficients
(3−2)sqrt
Subtract the numbers
sqrt
0+(sqrt×12÷sqrt)
Use the commutative property to reorder the terms
0+(12sqrt÷sqrt)
Divide the terms
More Steps

Evaluate
12sqrt÷sqrt
Rewrite the expression
sqrt12sqrt
Reduce the fraction
qrt12qrt
Reduce the fraction
rt12rt
Reduce the fraction
t12t
Reduce the fraction
112
Divide the terms
12
0+12
Solution
12
Show Solution

Find the excluded values
s=0,q=0,r=0,t=0
Evaluate
(((3sqrt×2)−(2sqrt×3))÷((3sqrt×2)+(2sqrt×3)))+(sqrt×12÷(sqrt×3−sqrt×2))
To find the excluded values,set the denominators equal to 0
(3sqrt×2)+(2sqrt×3)=0sqrt×3−sqrt×2=0
Solve the equations
More Steps

Evaluate
(3sqrt×2)+(2sqrt×3)=0
Simplify
More Steps

Evaluate
(3sqrt×2)+(2sqrt×3)
Multiply the terms
6sqrt+(2sqrt×3)
Multiply the terms
6sqrt+6sqrt
Collect like terms by calculating the sum or difference of their coefficients
(6+6)sqrt
Add the numbers
12sqrt
12sqrt=0
Evaluate
sqrt=0
Separate the equation into 4 possible cases
s=0q=0r=0t=0
Find the union
q=0r=0s=0t=0
s=0q=0r=0t=0sqrt×3−sqrt×2=0
Solve the equations
More Steps

Evaluate
sqrt×3−sqrt×2=0
Simplify
More Steps

Evaluate
sqrt×3−sqrt×2
Use the commutative property to reorder the terms
3sqrt−sqrt×2
Use the commutative property to reorder the terms
3sqrt−2sqrt
Collect like terms by calculating the sum or difference of their coefficients
(3−2)sqrt
Subtract the numbers
sqrt
sqrt=0
Separate the equation into 4 possible cases
s=0q=0r=0t=0
Find the union
q=0r=0s=0t=0
s=0q=0r=0t=0s=0q=0r=0t=0
Solution
s=0,q=0,r=0,t=0
Show Solution
