Question
Solve the equation
x∈∅
Alternative Form
No solution
Evaluate
(sqrt(x2+1)+sqrt(x2−1))÷(sqrt(x2+1)−sqrt(x2−1))=(2x2−1)÷2
Simplify
More Steps

Evaluate
(sqrt(x2+1)+sqrt(x2−1))÷(sqrt(x2+1)−sqrt(x2−1))
Add the terms
More Steps

Evaluate
sqrt(x2+1)+sqrt(x2−1)
Expand the expression
sqrtx2+sqrt+sqrt(x2−1)
Expand the expression
sqrtx2+sqrt+sqrtx2−sqrt
Add the terms
2sqrtx2+sqrt−sqrt
The sum of two opposites equals 0
2sqrtx2+0
Remove 0
2sqrtx2
2sqrtx2÷(sqrt(x2+1)−sqrt(x2−1))
Subtract the terms
More Steps

Simplify
sqrt(x2+1)−sqrt(x2−1)
Expand the expression
sqrtx2+sqrt−sqrt(x2−1)
Expand the expression
sqrtx2+sqrt−sqrtx2+sqrt
The sum of two opposites equals 0
0+sqrt+sqrt
Remove 0
sqrt+sqrt
Collect like terms by calculating the sum or difference of their coefficients
(1+1)sqrt
Add the numbers
2sqrt
2sqrtx2÷2sqrt
Rewrite the expression
2sqrt2sqrtx2
Reduce the fraction
2qrt2qrtx2
Reduce the fraction
2rt2rtx2
Reduce the fraction
2t2tx2
Reduce the fraction
22x2
Divide the terms
More Steps

Evaluate
22
Reduce the numbers
11
Calculate
1
x2
x2=(2x2−1)÷2
Rewrite the expression
x2=22x2−1
Cross multiply
x2×2=2x2−1
Simplify the equation
2x2=2x2−1
Cancel equal terms on both sides of the expression
0=−1
Solution
x∈∅
Alternative Form
No solution
Show Solution
