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peview Score Image Autodesk Autodesk 5IG IDEAS MATH Listen Simplify the expression, if possible. If the (x^(2)-3x-18)/(x^(2)-7x+6)=◻,x!=6

peview Score Image\newlineAutodesk\newlineAutodesk\newline55IG IDEAS MATH\newlineListen\newlineSimplify the expression, if possible. If the\newlinex2−3x−18x2−7x+6=□,x≠6 \frac{x^{2}-3 x-18}{x^{2}-7 x+6}=\square, x \neq 6

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Q. peview Score Image\newlineAutodesk\newlineAutodesk\newline55IG IDEAS MATH\newlineListen\newlineSimplify the expression, if possible. If the\newlinex2−3x−18x2−7x+6=□,x≠6 \frac{x^{2}-3 x-18}{x^{2}-7 x+6}=\square, x \neq 6
  1. Factor Numerator: Factor the numerator x2−3x−18x^2 - 3x - 18. This factors to (x−6)(x+3)(x - 6)(x + 3) because (x−6)(x+3)=x2+3x−6x−18=x2−3x−18(x - 6)(x + 3) = x^2 + 3x - 6x - 18 = x^2 - 3x - 18.
  2. Factor Denominator: Factor the denominator x2−7x+6x^2 - 7x + 6. This factors to (x−6)(x−1)(x - 6)(x - 1) because (x−6)(x−1)=x2−x−6x+6=x2−7x+6(x - 6)(x - 1) = x^2 - x - 6x + 6 = x^2 - 7x + 6.
  3. Cancel Common Term: Now, we have (x−6)(x+3)(x−6)(x−1)\frac{(x - 6)(x + 3)}{(x - 6)(x - 1)}. We can cancel out the (x−6)(x - 6) terms since x≠6x \neq 6.
  4. Simplify Expression: After canceling, the expression simplifies to (x+3)/(x−1)(x + 3)/(x - 1).

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