x-4 over x = 15 over x+4

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Start by cross-multiplying. You get (x - 4)(x + 4) = 15x. Since (a - b)(a + b) = a² - b², you get x² - 16 = 15x. Subtract 15x from both sides, and you have a quadratic equation: x² - 15x - 16. After factoring, you have (x + 1)(x - 16), and you set it equal to zero. Since just one of these (either (x + 1) or (x - 16)) needs to be equal to zero for the equation to equal 0, you find your two solutions by working each out. x + 1 = 0 becomes x = -1, and x - 16 = 0 becomes x = 16.                                                                                                              So, your solutions are (-1, 16)!                                                                                                                   You also have to check your original problem to find your exclusions, or x-values that are impossible, because the denominator cannot be equal to 0. On the left, x is by itself, and to get 0, x itself would have to be 0. On the right, you have x + 4. For this one, x cannot be equal to -4.                                                                   In other words, your solution set is (-1, 16) and x ≠ 0, x ≠ -4.                                                                   Hope I helped - hope you understand now :) edit