Evaluation Math Example 2

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Example 2

medium
Evaluate a2−b2a+b\frac{a^2 - b^2}{a + b} when a=5a = 5 and b=3b = 3.

Solution

  1. 1
    Substitute: 52−325+3=25−98=168\frac{5^2 - 3^2}{5 + 3} = \frac{25 - 9}{8} = \frac{16}{8}.
  2. 2
    Simplify: 168=2\frac{16}{8} = 2.
  3. 3
    Note: this works because a2−b2a+b=(a+b)(a−b)a+b=a−b=5−3=2\frac{a^2 - b^2}{a+b} = \frac{(a+b)(a-b)}{a+b} = a - b = 5 - 3 = 2.

Answer

22
Evaluating expressions with multiple variables requires substituting all values and following the order of operations. Recognizing algebraic structure (like difference of squares) can simplify the work.

About Evaluation

The process of calculating the numerical value of a mathematical expression by substituting specific numbers for each variable and then performing the indicated operations following the order of operations (PEMDAS/BODMAS).

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More Evaluation Examples

Example 1 easy

Evaluate [formula] when [formula].

Example 3 easy

Evaluate [formula] when [formula].

Example 4 hard

If [formula], find [formula].

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