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

(6x-13)=(4x+5)2x+1818/2=x=96(9)-13=414(9)+5=36...

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

Ответ:

alcott1110

17.03.2022

Mathematics

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFactoring

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

[Frac - Numerator] Factor quadratic: $\displaystyle \frac{(7x - 10)(x + 2)}{5x + 10}$ [Frac - Denominator] Factor GCF: $\displaystyle \frac{(7x - 10)(x + 2)}{5(x + 2)}$ [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.

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Simplify the fraction and state the excluded value(s). $\dfrac{7x^2+4x-20}{5x+10}$

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