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Simplify the fraction and state the excluded value(s).


[tex]\dfrac{7x^2+4x-20}{5x+10}[/tex]

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Answer:

[tex]\displaystyle \frac{7x^2 + 4x - 20}{5x + 10} = \frac{7x - 10}{5}, x \neq -2[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Algebra I

  • Terms/Coefficients
  • Factoring

Calculus

Discontinuities

  • Removable (Holes)
  • Jump (Piece-wise functions)
  • Infinite (Asymptotes)

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{7x^2 + 4x - 20}{5x + 10}[/tex]

Step 2: Simplify

  1. [Frac - Numerator] Factor quadratic:                    [tex]\displaystyle \frac{(7x - 10)(x + 2)}{5x + 10}[/tex]
  2. [Frac - Denominator] Factor GCF:                        [tex]\displaystyle \frac{(7x - 10)(x + 2)}{5(x + 2)}[/tex]
  3. [Frac] Divide/Simplify:                                           [tex]\displaystyle \frac{(7x - 10)}{5}, x \neq -2[/tex]

When we divide (x + 2), we would have a removable discontinuity. If we were to graph the original function, we would see at x = -2 there would be a hole in the graph.

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[tex]\color{skyblue}{\boxed{\tt{ANSWER:}}}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  8. Left to Right
  9. Algebra I

Terms/Coefficients

Factoring

Calculus

Discontinuities

  • Removable (Holes)
  • Jump (Piece-wise functions)
  • Infinite (Asymptotes)

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