3/(x-1)+4/(1-2x)?

enter image source here

1 Answer
turksvids
Jan 7, 2018

C. #(2x+1)/((x-1)(2x-1))#

Explanation:

We need to find a common denominator.

Start with:

#3/(x-1)+4/(1-2x)#

Common denominator:

#=3/(x-1)\*(1-2x)/(1-2x)+4/(1-2x)\*(x-1)/(x-1)#

Write as a single fraction:

#=(3(1-2x)+4(x-1))/((x-1)(1-2x))#

Expand in the numerator:

#=(3-6x+4x-4)/((x-1)(1-2x))#

Combine like terms in the numerator:

#=(-2x-1)/((x-1)(1-2x))#

Factor #-1# from numerator and from #1-2x# in the denominator:

#=((-1)(2x+1))/((x-1)(-1)(2x-1))#

Cancel the common #-1# factor:

#=(2x+1)/((x-1)(2x-1))#

Related questions
Impact of this question
451 views around the world
You can reuse this answer
Creative Commons License