Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are
and
.
Solution
Solve the equation
.
Solve the equation by following steps:
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 .
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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
.