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a\left(x+1\right)+b\left(x+1\right)-c\left(x+1\right)
Do the grouping ax+a+bx+b-cx-c=\left(ax+a\right)+\left(bx+b\right)+\left(-cx-c\right), and factor out a,b,-c in each of the groups respectively.
\left(x+1\right)\left(a+b-c\right)
Factor out common term x+1 by using distributive property.