simplify expressions

Question

Given the functions g(x)=2/2x-5, evaluate and SIMPLIFY each of the following expressions:

 

-6g(x)-1

 

 

Answer 1

Given the function g(x)=2/(2x-5), evaluate and SIMPLIFY the expression:

f(x) = -6g(x)-1

f(x) = -6(2/(2x-5))-1

f(x) = -12/(2x-5)-(2x-5)/(2x-5)

f(x) = (-12-(2x-5))/(2x-5)

f(x) = (-12-2x+5)/(2x-5)

f(x) = (-7-2x)/(2x-5)

f(x) = –(2x+7)/(2x-5) <== an answer

Divide by 2x-5:

2x+7 | 1
2x-5
––––
0+12

f(x) = –(1+12/(2x-5))

f(x) = –1–12/(2x-5) <== answer that’s simpler
because you can pick off the horizontal and vertical asymptotes: y = –1 and x = 5/2.

Also simpler to differentiate or integrate in later calculus course.

Answer 2

*backs away from the problem*

 

I apologize for getting in the way. 

Answer 3

g( x) = 2/ (2x -5 )    / you should place parenthesis

 

- 6 ( 2/(2x - 5 ) ) -1

 

  -12/ ( 2X -5 ) - 1 =

 

   -12/ (2x - 5 )-  ( 2x - 5 ) /( 2x - 5 ) = 

 

       (-12 -2x +5) / (2x -5 )

 

           ( -2x - 7 ) / ( 2x -5)