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

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

User Niezborala
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Answer:

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

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

User Rebecca Close
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