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Solve 0=x-1/(x-3)(x+2)

1 Answer

7 votes

Answer:

x = 2 + sqrt(6) or x = 2 - sqrt(6)

Step-by-step explanation by completing the square:

Solve for x:

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

0 = x - (x + 2)/(x - 3) is equivalent to x - (x + 2)/(x - 3) = 0:

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

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

(x^2 - 4 x - 2)/(x - 3) = 0

Multiply both sides by x - 3:

x^2 - 4 x - 2 = 0

Add 2 to both sides:

x^2 - 4 x = 2

Add 4 to both sides:

x^2 - 4 x + 4 = 6

Write the left hand side as a square:

(x - 2)^2 = 6

Take the square root of both sides:

x - 2 = sqrt(6) or x - 2 = -sqrt(6)

Add 2 to both sides:

x = 2 + sqrt(6) or x - 2 = -sqrt(6)

Add 2 to both sides:

Answer: x = 2 + sqrt(6) or x = 2 - sqrt(6)

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