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

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Answer 1 · 2017-05-23T14:54:26

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

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

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:
$(2(x^2+2x+1)-4)/((x+1))$

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

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

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

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