Solve for x:

[tex]0 = \frac{3x^{2} - 18x + 24}{x^{2} - 2x - 8}[/tex]

Please show your work.

D : x 2 − 2 x − 8  = 0 D : x 2 − 4 x + 2 x − 8  = 0 D : x ( x − 4 ) + 2 ( x − 4 )  = 0 D : ( x + 2 ) ( x − 4 )  = 0 D : x  = − 2 ∧ x  = 4 x 2 − 2 x − 8 3 x 2 − 18 x + 24 ​ = 0 ( x + 2 ) ( x − 4 ) 3 ( x 2 − 6 x + 8 ) ​ = 0 ( x + 2 ) ( x − 4 ) 3 ( x 2 − 4 x − 2 x + 8 ) ​ = 0 ( x + 2 ) ( x − 4 ) 3 ( x ( x − 4 ) − 2 ( x − 4 )) ​ = 0 ( x + 2 ) ( x − 4 ) 3 ( x − 2 ) ( x − 4 ) ​ = 0 ( x + 2 ) ( x − 4 ) 3 ( x − 2 ) ( x − 4 ) ​ = 0 ( x + 2 ) 3 ( x − 2 ) ​ = 0∣ ⋅ ( x + 2 ) 3 ( x − 2 ) = 0∣ : 3 x − 2 = 0 x = 2 ​

Answered by konrad509 | 2024-06-10

The solution to the equation is x = 2 , found by solving the numerator for zero and confirming that it does not make the denominator zero. The solution x = 4 is invalid as it results in a denominator of zero. Thus, the only valid solution is x = 2 .
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Answered by konrad509 | 2025-01-20