Answered

Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

help please, will give brainliest!
A. the equation has two true solutions
B. the equation had one true solution
C. the equation has one extraneous solution
D. the equation has one true solution and one extraneous solution ​

Help Please Will Give BrainliestA The Equation Has Two True Solutions B The Equation Had One True Solution C The Equation Has One Extraneous Solution D The Equa class=

Sagot :

mhanifa

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

manissaha129

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.

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.