{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-equation"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-equation-01","title":{"zh-Hant":"方程式：在定義域內解 x²/(x−1)=1/(x−1)","en":"Equation: solving x²/(x−1)=1/(x−1) inside its domain"},"summary":{"zh-Hant":"在允許範圍 ℝ 中，求方程 x²/(x−1)=1/(x−1) 的解集；並說明為什麼兩邊乘以 x−1 後得到的方程 x²=1 有兩個解，而原方程只有一個。","en":"With allowed domain ℝ, find the solution set of the equation x²/(x−1)=1/(x−1), and explain why the equation x²=1 obtained by multiplying both sides by x−1 has two solutions while the original has only one."},"mko_ids":["mko-equation"]}],"title":"Concept derivation guides"}