This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to find the value of x: Step 1: Set up the equation from the image. The equation is: (6)/(x-4) = (x+4)/(x) Step 2: Cross-multiply to eliminate the denominators. 6 · x = (x-4)(x+4) Step 3: Expand both sides of the equation. On the left side: 6x On the right side, use the difference of squares formula (a-b)(a+b) = a^2 - b^2: x^2 - 4^2 x^2 - 16 So the equation becomes: 6x = x^2 - 16 Step 4: Rearrange the equation into standard quadratic form ax^2 + bx + c = 0. Subtract 6x from both sides: 0 = x^2 - 6x - 16 x^2 - 6x - 16 = 0 Step 5: Factor the quadratic equation. We need two numbers that multiply to -16 and add to -6. These numbers are 2 and -8. (x+2)(x-8) = 0 Step 6: Set each factor equal to zero and solve for x. x+2 = 0 or x-8 = 0 x = -2 or x = 8 Step 7: Check for extraneous solutions. The original denominators are x-4 and x. If x=4, x-4=0, which is undefined. If x=0, x=0, which is undefined. Neither of our solutions, x=-2 or x=8, makes the denominators zero. Therefore, both solutions are valid. x = -2 or x = 8 3 done, 2 left today. You're making progress.