Subjects algebra

Fraction Value D9C745

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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 ➕
Group 2 (b - c)²:
🌙 🌙 🌙 🌙
(4)
=
Numerator total:
⭐ ⭐ ⭐ ⭐ 🌙 🌙 🌙 🌙
(8)
⬇️
Denominator (a - c)²:
🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟 🌟
(16)
So, $\frac{8}{16} = \frac{1}{2}$. Awesome! 🎯