How do you simplify #(2x + 10) /( x - 1) times (x^2 - 1) /( x + 5) - 4 /(x + 1)#?

1 Answer
May 23, 2017

Answer:

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

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

Explanation:

Factorise wherever possible.

#(2x + 10) /( x - 1) times (x^2 - 1) /( x + 5) - 4 /(x + 1)" "larr# there are 2 terms

#=color(blue)((2(x+5))/((x-1)) xx ((x+1)(x-1))/((x+5))) -color(red)(4/((x+1)))#

You may cancel in a term, as long as it is through a #xx# sign:

#=color(blue)((2cancel((x+5)))/cancel((x-1)) xx ((x+1)cancel((x-1)))/cancel((x+5))) -color(red)(4/((x+1)))#

#=color(blue)((2(x+1))/1) - color(red)(4/((x+1)))" "larr# find LCD and subtract

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

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

Expanding further gives:
#(2(x^2+2x+1)-4)/((x+1))#

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

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

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