Answer:
[tex]\frac{x+6}{x-1}[/tex]
Step-by-step explanation:
Given
[tex]\frac{x^2-3x-54}{x^2-10x+9}[/tex] ← factorise both numerator and denominator
= [tex]\frac{(x-9)(x+6)}{(x-9)(x-1)}[/tex] ← cancel (x - 9) on numerator/ denominator
= [tex]\frac{x+6}{x-1}[/tex] ← x ≠ 1
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[tex] \frac{ {x}^{2} - 3x - 54 }{ {x}^{2} - 10x + 9 } = \frac{(x - 9)(x + 6)}{(x - 9)(x - 1)} = \frac{x + 6}{x - 1} \\ [/tex]
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