$$ \frac{(3.63)^2 - (2.37)^2}{3.63 + 2.37} $$ is simplified to

### Concept & Formula This is a classic simplification problem relying on the difference of squares property. The denominator is designed to cancel out the addition factor of the expanded numerator. $$ \frac{a^2 - b^2}{a + b} = \frac{(a - b)(a + b)}{a + b} = a - b $$ ### Step-by-Step Solution * Identify the variables: $a = 3.63$ and $b = 2.37$. * The expression is in the exact format of $\frac{a^2 - b^2}{a + b}$. * Based on the algebraic identity, the $(a + b)$ terms in the numerator and denominator cancel each other out. * You are left with only $(a - b)$. * Calculate the difference: $$3.63 - 2.37 = 1.26$$ ### Exam Strategy & Shortcut Do not even write out the formula. When you see $\frac{a^2 - b^2}{a + b}$, your brain should immediately jump to calculating $a - b$. Perform the subtraction $3.63 - 2.37 = 1.26$ mentally. ### Common Pitfall A careless mistake during mental subtraction is the only real risk here (e.g., getting $1.36$ instead of $1.26$ by messing up the borrow/carry step in decimals). Always double-check your arithmetic! ### Final Answer Therefore, the correct answer is 1.26.