Question
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Ask by Newton Dawson. in the United States
Jan 13,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solutions are and .

Solution

Solve the equation .
Solve the equation by following steps:
  • step0: Solve for :
  • step1: Find the domain:
  • step2: Multiply both sides of the equation by LCD:
  • step3: Simplify the equation:
  • step4: Move the expression to the left side:
  • step5: Calculate:
  • step6: Factor the expression:
  • step7: Separate into possible cases:
  • step8: Solve the equation:
  • step9: Check if the solution is in the defined range:
  • step10: Find the intersection:
  • step11: Rewrite:

    The solutions to the equation are and .

Answered by UpStudy AI and reviewed by a Professional Tutor

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Simplify this solution

Extra Insights

To solve the equation , start by finding a common denominator for the left side, which is . Rewriting the equation gives:
This simplifies to . Now, cross-multiply to eliminate the fractions:
Expanding both sides yields:
Rearranging terms gives a quadratic equation:
Now, use the quadratic formula with , , and :
Calculating and :
So, or .
Thus, the solutions are and .

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