{"status": "success", "data": {"description_md": "For each pair of real numbers $a \\neq b$, define the [[operation]] $\\star$ as\n$(a \\star b) = \\frac{a+b}{a-b}$.\nWhat 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<br/>\n <span class=\"katex--inline\">(a \\star b) = \\frac{a+b}{a-b}</span> .<br/>\nWhat is the value of  <span class=\"katex--inline\">((1 \\star 2) \\star 3)</span> ?</p>\n<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>\n<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "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"}}