Solve this rational equation:
Х
1
x – 4
+
=
2
x2 - 6x + 8
x – 2

Hey there! :)

x = -1.

Step-by-step explanation:

Make each fraction have a common denominator:

Simplify:

Disregard the denominator and solve the numerators:

x - 2 + x² - 4x = 2

Combine like terms:

x² - 3x - 2 = 2

x² - 3x - 4 = 0

Factor:

(x - 4)(x + 1)

***Only one of these solutions works because if x = 4, the denominator of the first fraction would be 0, which is undefined. Therefore, the only possible solution is x = -1.

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step-by-step explanation: