**Core Concept**
Muscle relaxants are a class of medications used to relax muscles and relieve spasms. In patients with hepatic and renal failure, it's crucial to choose a muscle relaxant that is not metabolized or excreted by the liver or kidneys, to minimize the risk of toxicity.

**Why the Correct Answer is Right**
Rocuronium is a non-depolarizing muscle relaxant that is primarily metabolized by the liver and excreted by the kidneys. However, it has a unique property of being excreted mainly through biliary excretion, which makes it a safer choice in patients with hepatic and renal failure. This is because biliary excretion is less affected by kidney function compared to renal excretion.

**Why Each Wrong Option is Incorrect**
**Option A:** Succinylcholine is a depolarizing muscle relaxant that is metabolized by plasma cholinesterase, which is not affected by hepatic or renal function. However, it has a significant risk of causing hyperkalemia, which can be life-threatening in patients with renal failure.

**Option B:** Vecuronium is a non-depolarizing muscle relaxant that is metabolized by the liver and excreted by the kidneys. While it is a safe choice in patients with hepatic dysfunction, it may accumulate in patients with renal failure, leading to prolonged paralysis.

**Option C:** Atracurium is a non-depolarizing muscle relaxant that is metabolized by Hoffman elimination, a chemical process that is not affected by liver or kidney function. However, it can cause histamine release, leading to hypotension and other adverse effects.

**Clinical Pearl / High-Yield Fact**
When choosing a muscle relaxant in patients with hepatic and renal failure, consider the route of elimination (biliary vs. renal) and the potential for accumulation or toxicity.

**Correct Answer: C. Atracurium**