Part 4 of 4 (d) The ratio \( \frac{a-b}{a-b}=\square \), whereas the ratio \( \frac{a-b}{b-a}=\square \) provided that \( a \neq b \).

The ratio \( \frac{a-b}{a-b} = 1 \) as long as \( a \neq b \) ensures that you’re not dividing by zero. In essence, this reveals the self-duality of any non-zero quantity, where the same value over itself gives you a whole. On the other hand, the ratio \( \frac{a-b}{b-a} = -1 \) reflects the reversal of terms. Since \( b-a \) is simply \( -(a-b) \), this expression illustrates how flipping the order of subtraction switches the sign, reminding us that subtraction is not commutative, and that’s where the fun bits of algebra start to unfold!