adding rational expressions...simplest form

Question

__3x-7__  +  __-x+2__

  2x-6.              X-3

Answer 1

3x-7       -x+2

------  +  ------

2x-6         x-3

 

Like any fractions, to add these rational expressions you have to put them over a common denominator.  In this case, (2x-6) is exactly twice (x-3).  So all we have to do is multiply the second expression by 2/2:

 

3x-7        (-x+2) * 2

------   +   --------------

2x-6          (x-3) * 2

 

3x-7      -2x+4      3x-2x-7+4          x-3          1

------   +  ---------  =  -------------  =  --------  =  ---

2x-6         2x-6             2x-6            2(x-3)       2

Answer 2

Hi Carlos, hope this helps:

 

First you need to have a common denominator to add the equation together. You can do this by multiplying the second (-x+2)/(x-3) by 2 on the top and bottom. 

 

(3x-7)/(2x-6)+(-x+2)/(x-3)

=(3x-7) / (2(x-3)) + (-x+2) / (x-3) * 2/2

=(3x-7-2x+4) / (2(x-3))

= (x-3) / (2(x-3))

= 1/2

Answer 3

The expression can be written as 

 

(3x-7) / 2*(x-3)   +   (2-x) / (x-3)

 

= 3x - 7 - 2*(2-x)  /  x-3

= (5x - 11) / (x-3)