X-2/x-1=x+4/2x+2 show work

Answer:x = (i sqrt (7)) / 4 - 3/4 or x = - (i sqrt (7)) / 4 - 3/4 would be your answer

x = (i sqrt (7)) / 4 - 3/4 or x = - (i sqrt (7)) / 4 - 3/4

Step-by-step explanation:

Solve for x:

x - 1 - 2/x = 3 x + 2

Bring x - 1 - 2/x together using the common denominator x:

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

Multiply both sides by x:

x^2 - x - 2 = x (3 x + 2)

Expand out terms of the right hand side:

x^2 - x - 2 = 3 x^2 + 2 x

Subtract 3 x^2 + 2 x from both sides:

-2 x^2 - 3 x - 2 = 0

Divide both sides by - 2:

x^2 + (3 x) / 2 + 1 = 0

Subtract 1 from both sides:

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

Add 9/16 to both sides:

x^2 + (3 x) / 2 + 9/16 = - 7/16

Write the left hand side as a square:

(x + 3/4) ^2 = - 7/16

Take the square root of both sides:

x + 3/4 = (i sqrt (7)) / 4 or x + 3/4 = - (i sqrt (7)) / 4

Subtract 3/4 from both sides:

x = (i sqrt (7)) / 4 - 3/4 or x + 3/4 = - (i sqrt (7)) / 4

Subtract 3/4 from both sides:

Answer: x = (i sqrt (7)) / 4 - 3/4 or x = - (i sqrt (7)) / 4 - 3/4