Question

Solve
√x/x-1 + √x-1/x = 5/2
​

Answer 1

x = - 1  or  2  if  x/x-1 +x-1/x=5/2

Step-by-step explanation:

x/(x - 1)  + (x - 1)/x  = 5/2

Multiplying both sides by 2x(x-1)

=> 2x²  + 2(x - 1)² = 5x(x-1)

=> 2x² + 2(x² - 2x + 1) = 5x² - 5x

=> 2x² + 2x² - 4x + 2 = 5x² - 5x

=> 4x² - 4x + 2 = 5x² - 5x

=> x² - x - 2 = 0

=>x² - 2x + x - 2 = 0

=> x(x - 2) + 1(x - 2) = 0

=>(x + 1)(x - 2) = 0

=> x = - 1  or  2

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Answer 2

Step-by-step explanation:

x

+

x

x−1

=

2

5

⟹

x(x−1)

x

2

+(x−1)

2

=

2

5

⟹

x

2

−x

x

2

+x

2

−2x+1

=

2

5

⟹

x

2

−x

2x

2

−2x+1

=

2

5

⟹5(x

2

−x)=2(2x

2

−2x+1)

⟹5x

2

−5x=4x

2

−4x+2

⟹5x

2

−5x−4x

2

+4x−2=0

⟹x

2

−x−2=0

⟹x

2

−2x+x−2=0

⟹x(x−2)+1(x−2)=0

⟹(x+1)(x−2)=0

⟹x+1=0

So,x=−1

Again,x−2=0

Sox=2