Verified answer

2/(x + 1) + 3/(x - 1) = 5/(x² - 1)

(2x - 2 + 3x + 3)/(x² - 1) = 5/(x² - 1)

5x + 1 = 5

5x = 4

x = 4/5

Answer: x = 4/5

Proof:

2/(4/5 + 1) + 3/(4/5 - 1) = 5/([4/5]² - 1)

2/(4/5 + 5/5) + 3/(4/5 - 5/5) = 5/(16/25 - 25/25)

2/(9/5) + 3/(- 1/5) = 5/(- 9/25)

2(5/9) + 3(- 5) = 5(- 25/9)

10/9 - 15 = - 125/9

10/9 - 135/9 = - 125/9

- 125/9 = - 125/9

2/(x+1)+3/(x-1)=5/(x^2-1)

now solving you will get

2(x-1)+3(x+1)/(x^2-1)=5/(x^2-1)

cancelling out we get

5x-4=0

x=4/5

2/(x+1) + 3/(x-1) = 5/(x^2 - 1)

By taking LCM u get

(2x-2+3x+3)/(x^2 - 1) = 5(x^2 -1) || bcoz (a+b)(a-b) = (a^2 - b^2)

therefore 5x+1 = 5

5x = 4

x = 4/5

it's just simple fractions

note that the product of the two denominators on the left side of the equation is equal to the denominator on the right side