Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
v+2v3
Evaluate
v4v2−4vv−2
Multiply by the reciprocal
vv−2×v2−4v4
Rewrite the expression
vv−2×(v−2)(v+2)v4
Cancel out the common factor v−2
v1×v+2v4
Cancel out the common factor v
1×v+2v3
Solution
v+2v3
Show Solution
Find the excluded values
v=0,v=2,v=−2
Evaluate
v4v2−4vv−2
To find the excluded values,set the denominators equal to 0
v=0v4=0v4v2−4=0
The only way a power can be 0 is when the base equals 0
v=0v=0v4v2−4=0
Solve the equations
More Steps
Evaluate
v4v2−4=0
Cross multiply
v2−4=v4×0
Simplify the equation
v2−4=0
Move the constant to the right side
v2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
v=±4
Simplify the expression
More Steps
Evaluate
4
Write the number in exponential form with the base of 2
22
Reduce the index of the radical and exponent with 2
2
v=±2
Separate the equation into 2 possible cases
v=2v=−2
v=0v=0v=2v=−2
Solution
v=0,v=2,v=−2
Show Solution
Find the roots
v∈∅
Evaluate
v4v2−4vv−2
To find the roots of the expression,set the expression equal to 0
v4v2−4vv−2=0
Find the domain
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Evaluate
⎩⎨⎧v=0v4=0v4v2−4=0
The only way a power can not be 0 is when the base not equals 0
⎩⎨⎧v=0v=0v4v2−4=0
Calculate
More Steps
Evaluate
v4v2−4=0
Multiply both sides
v4v2−4×v4=0×v4
Evaluate
v2−4=0×v4
Multiply both sides
v2−4=0
Move the constant to the right side
v2=4
Take the root of both sides of the equation and remember to use both positive and negative roots
v=±4
Simplify the expression
v=±2
Separate the inequality into 2 possible cases
{v=2v=−2
Find the intersection
v∈(−∞,−2)∪(−2,2)∪(2,+∞)
⎩⎨⎧v=0v=0v∈(−∞,−2)∪(−2,2)∪(2,+∞)
Simplify
{v=0v∈(−∞,−2)∪(−2,2)∪(2,+∞)
Find the intersection
v∈(−∞,−2)∪(−2,0)∪(0,2)∪(2,+∞)
v4v2−4vv−2=0,v∈(−∞,−2)∪(−2,0)∪(0,2)∪(2,+∞)
Calculate
v4v2−4vv−2=0
Divide the terms
More Steps
Evaluate
v4v2−4vv−2
Multiply by the reciprocal
vv−2×v2−4v4
Rewrite the expression
vv−2×(v−2)(v+2)v4
Cancel out the common factor v−2
v1×v+2v4
Cancel out the common factor v
1×v+2v3
Multiply the terms
v+2v3
v+2v3=0
Cross multiply
v3=(v+2)×0
Simplify the equation
v3=0
The only way a power can be 0 is when the base equals 0
v=0
Check if the solution is in the defined range
v=0,v∈(−∞,−2)∪(−2,0)∪(0,2)∪(2,+∞)
Solution
v∈∅
Show Solution