$- x \cdot \frac{i}{1 - x i} = - \frac{i x}{- i x + 1}$

Explanation

- x \cdot \frac{i}{1 - x i} \overset{◯}{1} - \frac{i x}{- i x + 1}

①

Multiply $x$ by $\frac{i}{1 - i x}$ to get $\frac{i x}{- i x + 1}$ .

Step 1: Write $x$ as a fraction by putting $1$ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

x \cdot \frac{i}{1 - i x} Step 1 \frac{x}{1} \cdot \frac{i}{1 - i x} Step 2 \frac{x \cdot i}{1 \cdot ( 1 - i x )} = Step 3 \frac{i x}{1 - i x} = \frac{i x}{- i x + 1}

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−x⋅1−xii​=−−ix+1ix​

$- x \cdot \frac{i}{1 - x i} = - \frac{i x}{- i x + 1}$