Factorise wherever possible.
(2x + 10) /( x - 1) times (x^2 - 1) /( x + 5) - 4 /(x + 1)" "larr2x+10x−1×x2−1x+5−4x+1 ← there are 2 terms
=color(blue)((2(x+5))/((x-1)) xx ((x+1)(x-1))/((x+5))) -color(red)(4/((x+1)))=2(x+5)(x−1)×(x+1)(x−1)(x+5)−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))
