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# Please help me. This is the last question I don't understand. (11/2/19)

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Write the expression as a simplified rational expresion. Please show work. thank you so much for all you help!!!

Nov 3, 2018

#1
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\(\dfrac{\dfrac{4}{2x-1}+\dfrac{1}{4}}{x+1}=\\ \dfrac{\dfrac{16+2x-1}{4(2x-1)}}{x+1} = \\ \dfrac{15+2x}{4(2x-1)(x+1)}\)

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Nov 3, 2018
#2
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This is made more simple if we take numerator  and denominator separately

4                 1

_____    +   ____

2x - 1            4

4 (4)            +      1(2x - 1)                  16 + 1 (2x - 1)

_______            ________     =      _____________    =

4(2x - 1)               4 (2x - 1)                 4 ( 2x - 1)

16 + 2x - 1                     15   + 2x

__________   =              _________     =    a / 1

4 ( 2x - 1)                      4 ( 2x - 1)

Note that  we are now  dividing this result by  x + 1   which is the same as  (x + 1) / 1   =   b / 1

So.....we  have    [  a / 1  ]    ÷    [ b / 1]   =   [ a / 1 ]   x   [ 1 / b ]  =

15 + 2x                      1                      15  +  2x

_________   x      ______  =         _____________

4 (2x - 1)              x + 1               4(2x - 1) ( x + 1)   Nov 3, 2018