How do you find $f (x) + g (x), f (x) - g (x), f (x) \cdot g (x), (\frac{f}{g}) (x)$ $f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)$ given $f (x) = x + 3$ $f(x)=x+3$ and $g (x) = \frac{2 x}{x - 5}$ $g(x)=(2x)/(x-5)$ ?

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How do you find $f (x) + g (x), f (x) - g (x), f (x) \cdot g (x), (\frac{f}{g}) (x)$ $f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)$ given $f (x) = x + 3$ $f(x)=x+3$ and $g (x) = \frac{2 x}{x - 5}$ $g(x)=(2x)/(x-5)$ ?

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Answer 1 · 2017-03-09T19:29:42

$f (x) + g (x) = \frac{x^{2} - 15}{x - 5}$ $f(x)+g(x)=(x^2-15)/(x-5)$
$f (x) - g (x) = \frac{x^{2} - 4 x - 15}{x - 5}$ $f(x)-g(x)=(x^2-4x-15)/(x-5)$
$f (x) \cdot g (x) = \frac{2 x^{2} + 6 x}{x - 5}$ $f(x)*g(x)=(2x^2+6x)/(x-5)$
$\frac{f (x)}{g (x)} = \frac{x^{2} - 2 x - 15}{2 x}$ $f(x)/g(x)=(x^2-2x-15)/(2x)$

Explanation:

$f (x) + g (x) = x + 3 + \frac{2 x}{x - 5} = \frac{x^{2} - 5 x + 3 x - 15 + 2 x}{x - 5} = \frac{x^{2} - 15}{x - 5}$ $color(red)(f(x))+color(blue)(g(x))=color(red)(x+3)+color(blue)((2x)/(x-5))=(x^2-5x+3x-15+2x)/(x-5)=(x^2-15)/(x-5)$
$f (x) - g (x) = x + 3 - \frac{2 x}{x - 5} = \frac{x^{2} - 5 x + 3 x - 15 - 2 x}{x - 5} = \frac{x^{2} - 4 x - 15}{x - 5}$ $color(red)(f(x))-color(blue)(g(x))=color(red)(x+3)-color(blue)((2x)/(x-5))=(x^2-5x+3x-15-2x)/(x-5)=(x^2-4x-15)/(x-5)$
$f (x) \cdot g (x) = (x + 3) \cdot \frac{2 x}{x - 5} = \frac{2 x^{2} + 6 x}{x - 5}$ $color(red)(f(x))*color(blue)(g(x))=color(red)((x+3))*color(blue)((2x)/(x-5))=(2x^2+6x)/(x-5)$
$\frac{f (x)}{g (x)} = \frac{x + 3}{\frac{2 x}{x - 5}} = \frac{x^{2} - 5 x + 3 x - 15}{2 x} = \frac{x^{2} - 2 x - 15}{2 x}$ $color(red)(f(x))/color(blue)(g(x))=color(red)(x+3)/color(blue)((2x)/(x-5))=(x^2-5x+3x-15)/(2x)=(x^2-2x-15)/(2x)$

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How do you find $f (x) + g (x), f (x) - g (x), f (x) \cdot g (x), (\frac{f}{g}) (x)$ $f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)$ given $f (x) = x + 3$ $f(x)=x+3$ and $g (x) = \frac{2 x}{x - 5}$ $g(x)=(2x)/(x-5)$ ?

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How do you find f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)f(x)+g(x),f(x)−g(x),f(x)⋅g(x),(fg)(x)f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x) given f(x)=x+3f(x)=x+3f(x)=x+3 and g(x)=(2x)/(x-5)g(x)=2xx−5g(x)=(2x)/(x-5)?

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How do you find $f (x) + g (x), f (x) - g (x), f (x) \cdot g (x), (\frac{f}{g}) (x)$ $f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)$ given $f (x) = x + 3$ $f(x)=x+3$ and $g (x) = \frac{2 x}{x - 5}$ $g(x)=(2x)/(x-5)$ ?