Solve for all values of x. (x-5)/(x+3)=(-1)/(x) Answer: x=

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Solve for all values of  x.  (x-5)/(x+3)=(-1)/(x) Answer:  x=

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Identify Equation: First, we need to identify the equation we are solving: (x-5)/(x+3)=(-1)/(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+3) and x is x(x+3). We will multiply both sides of the equation by this common denominator to clear the fractions.Clear Fractions: Multiplying both sides of the equation by x(x+3), we get: (x-5)/(x+3) * x(x+3) = (-1)/(x) * x(x+3) This simplifies to: x(x-5) = -1(x+3)Distribute and Simplify: Now we distribute on both sides of the equation: x^2 - 5x = -x - 3Combine Like Terms: Next, we bring all terms to one side of the equation to set it equal to zero: x^2 - 5x + x + 3 = 0Factor Quadratic Equation: Combine like terms: x^2 - 4x + 3 = 0Solve for x: Now we factor the quadratic equation: (x - 3)(x - 1) = 0Check Solutions: Set each factor equal to zero and solve for x: x - 3 = 0 or x - 1 = 0Solving each equation gives us the values of x: x = 3 or x = 1However, we must check these solutions against the original equation to ensure they do not make any denominator zero. The original equation has denominators (x+3) and x, so we must exclude any solutions where x = -3 or x = 0.Checking the solutions, we see that neither x = 3 nor x = 1 makes any denominator zero, so both are valid solutions.

Solve for all values of $x$ . $\newline$ $\frac{x-5}{x+3}=\frac{-1}{x}$ $\newline$ Answer: $x=$

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Solve for all values of x x x.\newlinex−5x+3=−1x \frac{x-5}{x+3}=\frac{-1}{x} x+3x−5​=x−1​\newlineAnswer: x= x= x=

Solve for all values of $x$ . $\newline$ $\frac{x-5}{x+3}=\frac{-1}{x}$ $\newline$ Answer: $x=$