gloryyy3
Answered

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Which of the following is the product of the rational expressions shown below?

[tex]\[ \frac{x+2}{x-4} \cdot \frac{3x}{x+4} \][/tex]

A. [tex][tex]$\frac{3 x^2+6 x}{x^2-16}$[/tex][/tex]
B. [tex][tex]$\frac{3 x^2+2 x}{x-16}$[/tex][/tex]
C. [tex][tex]$\frac{4 x+2}{x^2}$[/tex][/tex]
D. [tex][tex]$\frac{3 x+6}{x^2-16}$[/tex][/tex]

Sagot :

GinnyAnswer
To find the product of the rational expressions [tex]\(\frac{x+2}{x-4} \cdot \frac{3 x}{x+4}\)[/tex], we follow these steps:

1. Multiply the numerators together:
[tex]\[ (x + 2) \cdot (3x) \][/tex]

2. Multiply the denominators together:
[tex]\[ (x - 4) \cdot (x + 4) \][/tex]

Let's start with the numerator:
[tex]\[ (x + 2)(3x) = 3x(x + 2) = 3x^2 + 6x \][/tex]

Now for the denominator, notice that we have a difference of squares:
[tex]\[ (x - 4)(x + 4) = x^2 - 16 \][/tex]

Putting these together, we get the product of the rational expressions:
[tex]\[ \frac{(x + 2) \cdot (3x)}{(x - 4) \cdot (x + 4)} = \frac{3x^2 + 6x}{x^2 - 16} \][/tex]

Hence, the correct option is:
[tex]\[ \mathbf{A.} \frac{3x^2 + 6x}{x^2 - 16} \][/tex]
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