{"status": "success", "data": {"description_md": "For each pair of real numbers $a \\neq b$, define the operation $\\star$ as $$(a \\star b) = \\frac{a+b}{a-b}.$$ What is the value of $((1 \\star 2) \\star 3)$?\n\n$\\mathrm{(A) \\ } -\\frac{2}{3}\\qquad \\mathrm{(B) \\ } -\\frac{1}{5} \\qquad \\mathrm{(C) \\ } 0\\qquad \\mathrm{(D) \\ } \\frac{1}{2}\\qquad \\mathrm{(E) \\ } \\textrm{This value is not defined.}$", "description_html": "<p>For each pair of real numbers <span class=\"katex--inline\">a \\neq b</span>, define the operation <span class=\"katex--inline\">\\star</span> as <span class=\"katex--display\">(a \\star b) = \\frac{a+b}{a-b}.</span> What is the value of <span class=\"katex--inline\">((1 \\star 2) \\star 3)</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A) \\ } -\\frac{2}{3}\\qquad \\mathrm{(B) \\ } -\\frac{1}{5} \\qquad \\mathrm{(C) \\ } 0\\qquad \\mathrm{(D) \\ } \\frac{1}{2}\\qquad \\mathrm{(E) \\ } \\textrm{This value is not defined.}</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2005 AMC 10A Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/05_amc10A_p03", "prev": "/problem/05_amc10A_p01"}}