What is the answer to a= 1/((sqrt(a)-1))-1/((sqrt(a)+1))+1 ?

The answer to a= 1/((sqrt(a)-1))-1/((sqrt(a)+1))+1 is a=1+sqrt(2)

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a= 1/((sqrt(a)-1))-1/((sqrt(a)+1))+1

a = \frac{1}{( a - 1 )} - \frac{1}{( a + 1 )} + 1

a = 1 + 2

Decimal Notation

a = 2.41421 \dots

Solution steps

a = \frac{1}{( a - 1 )} - \frac{1}{( a + 1 )} + 1

Find Least Common Multiplier of

a - 1, a + 1 : (a - 1) (a + 1)

Multiply by LCM=

(a - 1) (a + 1)

a (a - 1) (a + 1) = \frac{1}{a - 1} (a - 1) (a + 1) - \frac{1}{a + 1} (a - 1) (a + 1) + 1 \cdot (a - 1) (a + 1)

Simplify

a (a - 1) (a + 1) = a + 1 - (a - 1) + (a - 1) (a + 1)

Expand

a (a - 1) (a + 1) : a^{2} - a

Expand

a + 1 - (a - 1) + (a - 1) (a + 1) : a + 1

a^{2} - a = a + 1

Solve

a^{2} - a = a + 1 : a = 1 + 2, a = 1 - 2

a = 1 + 2, a = 1 - 2

Verify Solutions:

a = 1 + 2

True

, a = 1 - 2

False

The solution is

a = 1 + 2

\frac{72}{( x ^{\frac{8}{5}} )} = \frac{( x ^{\frac{7}{5}} )}{24}

x^{\frac{1}{2}} - 8 x^{\frac{1}{4}} + 15 = 0

x^{2} - x = 3 - x

x + 2 x - 1 = 2

2 x^{2} - 2 6 x + 3 = 0

What is the answer to a= 1/((sqrt(a)-1))-1/((sqrt(a)+1))+1 ?
The answer to a= 1/((sqrt(a)-1))-1/((sqrt(a)+1))+1 is a=1+sqrt(2)
Solve for a: a= 1/((sqrt(a)-1))-1/((sqrt(a)+1))+1
The solution is a=1+sqrt(2)