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Elden [556K]
3 years ago
15

For the rational expression 2x^2-7x-15/x^2-25, do both of the following,

Mathematics
1 answer:
Mrrafil [7]3 years ago
3 0

Answer:

a. \frac{2x + 3}{x+5}

b. x ≠ -5 (Vertical asymptote) and x ≠ 5 (Hole)

Step-by-step explanation:

Factor the numerator (Grouping):

2x^2 - 7x - 15              

Two numbers that multiply to -30 and add to -7 = -3 and 10

[2x^2 - 10x] + [3x - 15]

(2x + 3)(x - 5)

Factor the denominator (Difference of Two Squares):

x^2 - 25 = (x +5)(x-5)

Factored Expression:

(x - 5) can be factored out of top and bottom as a hole-

\frac{(2x + 3)(x - 5)}{(x + 5)(x - 5)} = \frac{2x + 3}{x+5}

Variable Restrictions:

Denominator ≠ 0

x + 5 = 0\\x = -5

Vertical asymptote at x = -5 ⇒ x ≠ -5

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