8/1-x^2+5/x+1= 4/x-1

8 / (1 - x^2) + 5 / (x + 1) = 4 / (x - 1)

-8 / (x^2 - 1) + 5 / (x + 1) = 4 / (x - 1)

-8 /((x + 1)(x - 1)) + 5 / (x + 1) = 4 / (x - 1)

Can’t divide by zero, so x ≠ ± 1.

Multiply both sides by (x + 1)(x - 1):

-8 + 5(x - 1) = 4(x + 1)

-8 + 5x - 5 = 4x + 4

Add -4x + 13 to both sides:

x = 17

check:

8 / (1 - (17)^2) + 5 / ((17) + 1) =? 4 / ((17) - 1)

8/((1 + 17)(1 - 17)) + 5/18 =? 4/16

8/((18)(-16)) + 5/18 =? 1/4

-1/((18)(2)) + 2*5/(2*18) =? 1/4

9/(2*18) = 1/4 √

-8 / (x^2 - 1) + 5 / (x + 1) = 4 / (x - 1)

-8 /((x + 1)(x - 1)) + 5 / (x + 1) = 4 / (x - 1)

Can’t divide by zero, so x ≠ ± 1.

Multiply both sides by (x + 1)(x - 1):

-8 + 5(x - 1) = 4(x + 1)

-8 + 5x - 5 = 4x + 4

Add -4x + 13 to both sides:

x = 17

check:

8 / (1 - (17)^2) + 5 / ((17) + 1) =? 4 / ((17) - 1)

8/((1 + 17)(1 - 17)) + 5/18 =? 4/16

8/((18)(-16)) + 5/18 =? 1/4

-1/((18)(2)) + 2*5/(2*18) =? 1/4

9/(2*18) = 1/4 √

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