Solve for all values of x. (x-5)/(x+9)=(4)/(x) Answer: x=

Question

Solve for all values of  x.  (x-5)/(x+9)=(4)/(x) Answer:  x=

Bytelearn · Accepted Answer

Identify Equation: First, we need to identify the equation we are solving: (x-5)/(x+9)=(4)/(x). We want to find all values of x that satisfy this equation.Cross-Multiply to Eliminate Fractions: To solve the equation, we will cross-multiply to eliminate the fractions: (x - 5) * x = 4 * (x + 9).Distribute and Simplify: Now, we distribute on both sides of the equation: x^2 - 5x = 4x + 36.Bring Terms Together: Next, we bring all terms to one side to set the equation to zero: x^2 - 5x - 4x - 36 = 0.Factor or Use Quadratic Formula: Combine like terms: x^2 - 9x - 36 = 0.Set Factors Equal to Zero: Now, we need to factor the quadratic equation, if possible, or use the quadratic formula to find the values of x. Let's try to factor first: (x - 12)(x + 3) = 0.Solve for x: We set each factor equal to zero and solve for x: x - 12 = 0 or x + 3 = 0.Check for Extraneous Solutions: Solving the first equation gives us x = 12. Solving the second equation gives us x = -3.Check x = 12: However, we must check for extraneous solutions by plugging these values back into the original equation, because the original equation has restrictions on the values of x (x cannot be 0 or -9, as these would make the denominators zero).Check x = -3: Checking x = 12: (12-5)/(12+9) = 7/21 = 1/3 and (4)/(12) = 1/3. The original equation holds true for x = 12.Checking x = -3: (-3-5)/(-3+9) = -8/6 = -4/3 and (4)/(-3) = -4/3. The original equation holds true for x = -3.

Solve for all values of $x$ . $\newline$ $\frac{x-5}{x+9}=\frac{4}{x}$ $\newline$ Answer: $x=$

Full solution

More problems from Find the roots of factored polynomials

Related topics

Solve for all values of x x x.\newlinex−5x+9=4x \frac{x-5}{x+9}=\frac{4}{x} x+9x−5​=x4​\newlineAnswer: x= x= x=

Solve for all values of $x$ . $\newline$ $\frac{x-5}{x+9}=\frac{4}{x}$ $\newline$ Answer: $x=$