|x|+| x/((x-1))|=((x^2))/(|x-1|)

解

∣ x ∣ + \frac{x}{( x - 1 )} = \frac{( x ^{2} )}{∣ x - 1 ∣}

x = 0 or x \geq 1

解答ステップ

∣ x ∣ + \frac{x}{( x - 1 )} = \frac{( x ^{2} )}{∣ x - 1 ∣}

簡素化

∣ x ∣ + \frac{∣ x ∣}{∣ x - 1 ∣} = \frac{x ^{2}}{∣ x - 1 ∣}

以下で両辺を乗じる:

∣ x - 1 ∣

∣ x ∣ ∣ x - 1 ∣ + ∣ x ∣ = x^{2}

解く

∣ x ∣ ∣ x - 1 ∣ + ∣ x ∣ = x^{2} : x = 0 or x \geq 1

x = 0 or x \geq 1