Question

Simplificati: $\frac{(3x+5)(x-1)^{2}-4(3x+5) }{(x+1)^{2}(x-3) }$

Answer 1

$\frac{(3x+5)(x-1)^{2}-4(3x+5) }{(x+1)^{2}(x-3)}=\frac{(3x+5)[(x-1)^{2}-4])}{(x+1)^{2} (x-3)}=$

a²-b²=(a-b)*(a+b)

$\frac{(3x+5)[(x-1)^{2}-2^{2} ])}{(x+1)^{2} (x-3)}=\frac{(3x+5)[(x-1-2)(x-1+2)])}{(x+1)^{2} (x-3)}=\frac{(3x+5)(x-3)(x+1)}{(x+1)^{2} (x-3)}= \frac{3x+5}{x+1}$