Question

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

Answer 1

Answer:

$\displaystyle \frac{7x^2 + 4x - 20}{5x + 10} = \frac{7x - 10}{5}, x \neq -2$

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

$\displaystyle \frac{7x^2 + 4x - 20}{5x + 10}$

Step 2: Simplify

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

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.