Solve for all values of x. (x-8)/(x+4)=(-2)/(x) Answer: x=

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Solve for all values of  x.  (x-8)/(x+4)=(-2)/(x) Answer:  x=

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Identify Equation: First, we need to identify the equation we are solving: (x-8)/(x+4)=(-2)/(x). We will solve for x by finding a common denominator and then cross-multiplying to eliminate the fractions.Find Common Denominator: The common denominator between (x+4) and x is x(x+4). We will cross-multiply to get rid of the fractions: (x - 8) * x = (-2) * (x + 4).Cross-Multiply: Now we distribute on both sides of the equation: x(x) - 8x = -2x - 8.Distribute and Simplify: Simplify the equation by combining like terms: x^2 - 8x = -2x - 8.Bring Terms Together: To solve for x, we need to bring all terms to one side of the equation to set it equal to zero: x^2 - 8x + 2x + 8 = 0.Combine Like Terms: Combine like terms: x^2 - 6x + 8 = 0.Factor Quadratic Equation: Now we factor the quadratic equation: (x - 4)(x - 2) = 0.Set Factors Equal: Set each factor equal to zero and solve for x: x - 4 = 0 or x - 2 = 0.Solve for x: Solving the first equation for x gives us x = 4. Solving the second equation for x gives us x = 2.Check Valid Solutions: However, we must check these solutions against the original equation to ensure they do not make any denominator zero. The original equation has denominators (x+4) and x, so x cannot be -4 or 0.Check x = 4: Checking x = 4: Since 4 is not -4 or 0, it does not make any denominator zero, so x = 4 is a valid solution.Check x = 2: Checking x = 2: Since 2 is not -4 or 0, it does not make any denominator zero, so x = 2 is a valid solution.

Solve for all values of $x$ . $\newline$ $\frac{x-8}{x+4}=\frac{-2}{x}$ $\newline$ Answer: $x=$

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Solve for all values of $x$ . $\newline$ $\frac{x-8}{x+4}=\frac{-2}{x}$ $\newline$ Answer: $x=$