Math  /  Algebra

QuestionSolve. 2z+9=1z6\frac{2}{z+9}=\frac{1}{z-6}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution(s) is/are z=z= \square \square. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There is no solution.

Studdy Solution
Check for extraneous solutions by substituting z=21 z = 21 back into the original equation to ensure it does not result in division by zero:
Original equation:
2z+9=1z6 \frac{2}{z+9} = \frac{1}{z-6}
Substitute z=21 z = 21 :
221+9=1216 \frac{2}{21+9} = \frac{1}{21-6}
230=115 \frac{2}{30} = \frac{1}{15}
Both sides simplify to 115 \frac{1}{15} , confirming z=21 z = 21 is a valid solution.
The solution is:
A. The solution(s) is/are z=21 z = 21 .

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