Let's solve this step by step! 🎉
1️⃣ We know $a - b = 2$ and $b - c = 2$.
2️⃣ Let's find $a - c$.
Since $a - c = (a - b) + (b - c)$, that means:
$$a - c = 2 + 2 = 4$$
3️⃣ Now, let's write the fraction:
$$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2} = \frac{2^2 + 2^2}{4^2}$$
4️⃣ Calculate the squares:
$$= \frac{4 + 4}{16}$$
5️⃣ Add the top:
$$= \frac{8}{16}$$
6️⃣ Simplify the fraction:
$$= \frac{1}{2}$$
Great job! The answer is $\frac{1}{2}$ or 0.5.
Imagine you have groups of big stars ⭐⭐ and big moons 🌙 to show the numbers!
Group 1 (a - b)²:
⭐ ⭐ ⭐ ⭐
(4)
Add ➕
⭐ ⭐ ⭐ ⭐
(4)
Group 2 (b - c)²:
🌙 🌙 🌙 🌙
(4)
=
🌙 🌙 🌙 🌙
(4)
Numerator total:
⭐ ⭐ ⭐ ⭐ 🌙 🌙 🌙 🌙
(8)
⬇️
⭐ ⭐ ⭐ ⭐ 🌙 🌙 🌙 🌙
(8)
Denominator (a - c)²:
🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟
(16)
So, $\frac{8}{16} = \frac{1}{2}$.
Awesome! 🎯🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟
(16)