Math Problem Statement

The expression is \(\frac{a^2 + 4a + 7b}{5 - a^3}\) where \(a = 2\) and \(b = 6\).

Solution

The expression you provided is:

a2+4a+7b5a3\frac{a^2 + 4a + 7b}{5 - a^3}

where a=2a = 2 and b=6b = 6. We can substitute these values into the expression to find the result.

Let me compute this for you.The value of the expression a2+4a+7b5a3\frac{a^2 + 4a + 7b}{5 - a^3} when a=2a = 2 and b=6b = 6 is 18-18.

Would you like more details on the steps, or do you have any questions?

Here are 5 related questions to explore:

  1. How does the value change if a=3a = 3 and b=5b = 5?
  2. What happens if the denominator becomes 0, and why is this problematic?
  3. How would this expression change if you added a constant to both the numerator and the denominator?
  4. Can you simplify this expression algebraically before substituting the values?
  5. How can you graph the function represented by this expression for varying values of aa and bb?

Tip: Always check if the denominator in a rational expression equals zero to avoid undefined results.

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Math Problem Analysis

Mathematical Concepts

Algebra
Substitution
Rational Expressions

Formulas

Substitute values into algebraic expressions
Formula for evaluating rational expressions

Theorems

Basic algebraic manipulation and simplification rules

Suitable Grade Level

Grades 8-10