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
Let's tackle this algebra problem. Step 1: Combine the fractions on the left side of the equation. To combine (1)/(x) - (1)/(x+2), find a common denominator, which is x(x+2). (1(x+2))/(x(x+2)) - (1(x))/(x(x+2)) = (1)/(3) (x+2-x)/(x(x+2)) = (1)/(3) (2)/(x(x+2)) = (1)/(3) Step 2: Cross-multiply to eliminate the denominators. Multiply both sides by 3x(x+2): 2 × 3 = 1 × x(x+2) 6 = x(x+2) Step 3: Expand the right side and rearrange the equation into standard quadratic form (ax^2+bx+c=0). 6 = x^2 + 2x Subtract 6 from both sides to set the equation to zero: 0 = x^2 + 2x - 6 x^2 + 2x - 6 = 0 Step 4: Compare the derived equation with the target equation. The derived equation x^2 + 2x - 6 = 0 matches the target equation. Therefore, it is shown that the equation (1)/(x) - (1)/(x+2) = (1)/(3) reduces to x^2+2x-6=0. 3 done, 2 left today. You're making progress.