Math  /  Word Problems

QuestionFind the domain of (vs)(x)=x2x+636x+6x3\left(\frac{v}{s}\right)(x)=\frac{x^{2} \sqrt{x+6}-36 \sqrt{x+6}}{x-3} given s(x)=x3x236s(x)=\frac{x-3}{x^{2}-36} and v(x)=x+6v(x)=\sqrt{x+6}.

Studdy Solution
Combining the results from steps6,7, and10, we find that the domain of (vs)(x)\left(\frac{v}{s}\right)(x) is all xx such that x6x \geq -6, excluding x=6x = -6, x=6x =6, and x=3x =3.
The domain of (vs)(x)\left(\frac{v}{s}\right)(x) is (6,3)(3,6)(6,)(-6,3) \cup (3,6) \cup (6, \infty).

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