$\frac{40}{1 - j} - 1 = \frac{j + 39}{- j + 1}$

Explanation

\frac{40}{1 - j} - 1 \overset{◯}{1} \frac{j + 39}{- j + 1}

①

Subtract $1$ from $\frac{40}{1 - j}$ to get $\frac{j + 39}{- j + 1}$ .

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

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the second fraction by $- j + 1$ .

\frac{40}{1 - j} - 1 Step 1 \frac{40}{1 - j} - \frac{1}{1} = \frac{40}{1 - j} - \frac{1 \cdot ( - j + 1 )}{1 \cdot ( - j + 1 )} = Step 2 \frac{40}{1 - j} - \frac{- j + 1}{1 - j} = \frac{40 - ( - j + 1 )}{- j + 1} = = \frac{j + 39}{- j + 1}

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1−j40​−1=−j+1j+39​

$\frac{40}{1 - j} - 1 = \frac{j + 39}{- j + 1}$