Question

Question:

Answer 1

Answer:

x = 3/2 + sqrt(17)/2 or x = 3/2 - sqrt(17)/2

Step-by-step explanation:

Solve for x over the real numbers:

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

x/x - 1 = 0:

0 = x - 3 - 2/x

0 = x - 3 - 2/x is equivalent to x - 3 - 2/x = 0:

x - 3 - 2/x = 0

Bring x - 3 - 2/x together using the common denominator x:

(x^2 - 3 x - 2)/x = 0

Multiply both sides by x:

x^2 - 3 x - 2 = 0

Add 2 to both sides:

x^2 - 3 x = 2

Add 9/4 to both sides:

x^2 - 3 x + 9/4 = 17/4

Write the left hand side as a square:

(x - 3/2)^2 = 17/4

Take the square root of both sides:

x - 3/2 = sqrt(17)/2 or x - 3/2 = -sqrt(17)/2

Add 3/2 to both sides:

x = 3/2 + sqrt(17)/2 or x - 3/2 = -sqrt(17)/2

Add 3/2 to both sides:

Answer: x = 3/2 + sqrt(17)/2 or x = 3/2 - sqrt(17)/2