[tex]x {}^{2} - {y}^{2} + x - y = (x + y)(x - y) + (x - y) = (x - y)(x + y + 1)[/tex]

Verified answer

[tex]\displaystyle\bf\\x^{2} - y^{2} +x-y=(x^{2} - y^{2} )+(x-y)=(x-y)\cdot(x+y)+(x-y)=\\\\\\=(x-y)\cdot(x+y+1)[/tex]