Solve for all values of x. (x-7)/(x-3)=(-2)/(x) Answer: x=

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Solve for all values of  x.  (x-7)/(x-3)=(-2)/(x) Answer:  x=

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Set Up Equation: First, we need to set up the equation given by the problem: (x-7)/(x-3) = (-2)/x. To solve for x, we will cross-multiply to eliminate the fractions.Cross-Multiply: Cross-multiplying gives us: (x - 7) * x = (-2) * (x - 3). This will allow us to create a quadratic equation.Expand Equation: Expanding both sides of the equation, we get: x^2 - 7x = -2x + 6. This simplifies the equation and prepares it for further manipulation.Move Terms: Next, we will move all terms to one side of the equation to set it equal to zero: x^2 - 7x + 2x - 6 = 0.Factor Quadratic: Combining like terms, we get: x^2 - 5x - 6 = 0. This is the quadratic equation we need to solve for x.Set Equal to Zero: To solve the quadratic equation, we can factor it: (x - 6)(x + 1) = 0.Solve for x: Setting each factor equal to zero gives us the potential solutions for x: x - 6 = 0 or x + 1 = 0.Check Solutions: Solving each equation for x gives us the solutions: x = 6 or x = -1.Check x = 6: However, we must check these solutions against the original equation to ensure they do not make any denominator equal to zero, as that would be undefined.Check x = -1: Checking x = 6: The original equation's denominators are (6 - 3) and 6, neither of which is zero, so x = 6 is a valid solution.Checking x = -1: The original equation's denominators are (-1 - 3) and -1, neither of which is zero, so x = -1 is also a valid solution.

Solve for all values of $x$ . $\newline$ $\frac{x-7}{x-3}=\frac{-2}{x}$ $\newline$ Answer: $x=$

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Solve for all values of $x$ . $\newline$ $\frac{x-7}{x-3}=\frac{-2}{x}$ $\newline$ Answer: $x=$