Solve for all values of x. (x+1)/(x-5)=(-2)/(x) Answer: x=

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Solve for all values of  x.  (x+1)/(x-5)=(-2)/(x) Answer:  x=

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Cross-Multiply: First, we need to cross-multiply to eliminate the fractions and get a clearer equation to work with. (x + 1) * x = (-2) * (x - 5)Distribute Terms: Now, we distribute the terms on both sides of the equation. x^2 + x = -2x + 10Bring Terms Together: Next, we bring all terms to one side of the equation to set it equal to zero and solve for x. x^2 + x + 2x - 10 = 0Combine Like Terms: Combine like terms to simplify the equation. x^2 + 3x - 10 = 0Factor Quadratic Equation: Now, we need to factor the quadratic equation, if possible, to find the values of x. (x + 5)(x - 2) = 0Set Factors Equal: Set each factor equal to zero and solve for x. x + 5 = 0 or x - 2 = 0Solve for x (1): Solve the first equation for x. x = -5Solve for x (2): Solve the second equation for x. x = 2Check Solutions: We must check the solutions to ensure they do not make the original equation undefined by making the denominator zero. For x = -5, the original equation becomes (-5+1)/(-5-5)=(-2)/(-5), which is valid. For x = 2, the original equation becomes (2+1)/(2-5)=(-2)/(2), which is also valid.

Solve for all values of $x$ . $\newline$ $\frac{x+1}{x-5}=\frac{-2}{x}$ $\newline$ Answer: $x=$

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Solve for all values of $x$ . $\newline$ $\frac{x+1}{x-5}=\frac{-2}{x}$ $\newline$ Answer: $x=$