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Sagot :
Answer:
- C. the equation has one extraneous solution
Step-by-step explanation:
Given equation:
- x/(x - 1) + 2/(x + 2) = -6/(x² + x - 2)
Common denominator is x² + x - 2, consider x ≠ 1 and x≠ -2
Multiply both sides by x² + x - 2:
- x(x + 2) + 2(x - 1) = -6
- x² + 2x + 2x - 2 + 6 = 0
- x² + 4x + 4 = 0
- (x + 2)² = 0
- x + 2 = 0
- x = -2
There is one solution but it is not true one.
Option C is correct
Answer:
[tex] \frac{x}{x - 1} + \frac{2}{x + 2} = \frac{ - 6}{ {x}^{2} + x - 2 } \\ \frac{x(x + 2) + 2(x - 1)}{(x - 1)(x + 2)} = \frac{ - 6}{ {x}^{2} + x - 2} \\ \frac{ {x}^{2} + 2x + 2x - 2 }{ {x}^{2} + 2x - x - 2} = \frac{ - 6}{ {x}^{2} + x - 2} \\ \frac{ {x}^{2} + 4x - 2 }{ {x}^{2} + x - 2} = \frac{ - 6}{ {x}^{2} + x - 2 } \\ {x}^{2} + 4x - 2 = - 6 \\ {x}^{2} + 4x + 4 = 0 \\ {x}^{2} + 2 \times 2 \times x + {2}^{2} = 0 \\ {(x + 2)}^{2} = 0 \\ x + 2 = 0 \\ \boxed{x = - 2 }[/tex]
x =-2 is the right answer.
C. the equation has one extraneous solution.
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