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

1 Answer
Gerardina C.
Mar 9, 2017

#f(x)+g(x)=(x^2-15)/(x-5)#
#f(x)-g(x)=(x^2-4x-15)/(x-5)#
#f(x)*g(x)=(2x^2+6x)/(x-5)#
#f(x)/g(x)=(x^2-2x-15)/(2x)#

Explanation:

#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)#
#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)#
#color(red)(f(x))*color(blue)(g(x))=color(red)((x+3))*color(blue)((2x)/(x-5))=(2x^2+6x)/(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^2-2x-15)/(2x)#

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