Find the domain of y=(x+3)/(4-sqrt(x^(2)-9))

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Find the domain of  y=(x+3)/(4-sqrt(x^(2)-9))

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Identify Restrictions: Identify the restrictions for the denominator, since division by zero is undefined. 4 - sqrt(x^2 - 9) ≠ 0Solve Denominator: Solve for x where the denominator equals zero. sqrt(x^2 - 9) = 4Square Root Elimination: Square both sides to eliminate the square root. (x^2 - 9) = 16Move to Right Side: Move 9 to the right side. x^2 = 25Take Square Root: Take the square root of both sides. x = ±5Check Solutions: Since we squared during our steps, we need to check if these solutions don't cause the original denominator to be zero. Plug x = 5 and x = -5 back into the original denominator. 4 - sqrt(5^2 - 9) = 4 - sqrt(16) = 4 - 4 = 0 4 - sqrt((-5)^2 - 9) = 4 - sqrt(16) = 4 - 4 = 0 Both x = 5 and x = -5 make the denominator zero, so they are not in the domain.Identify Square Root Restrictions: Identify the restrictions for the square root in the denominator, since square roots are only defined for non-negative numbers. x^2 - 9 ≥ 0Factor and Solve: Factor the left side. (x + 3)(x - 3) ≥ 0Find Intervals: Find the intervals where the inequality is satisfied. x ≤ -3 or x ≥ 3Combine Restrictions: Combine the restrictions from the denominator and the square root. The domain is all x such that x ≤ -3 or x ≥ 3, but not including x = 5 or x = -5.

Find the domain of $\newline$ $y=\frac{x+3}{4-\sqrt{x^{2}-9}}$

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Find the domain of $\newline$ $y=\frac{x+3}{4-\sqrt{x^{2}-9}}$