Question

Help me with this please

Answer 1

`\large\boxed{(b)\ (x+2)/(x-3)}`

Explanation:

`(1)/(x+1)+(x)/(x-3)-(-x-5)/(x^2-2x-3)=(*)\\\\x^2-2x-3=x^2-3x+x-3=x(x-3)+1(x-3)=(x-3)(x+1)\\\\(*)=(1(x-3))/((x+1)(x-3))+(x(x+1))/((x+1)(x-3))+(-(-x-5))/((x+1)(x-3))\\\\=(x-3+x^2+x+x+5)/((x+1)(x-3))=(x^2+(x+x+x)+(-3+5))/((x+1)(x-3))\\\\=(x^2+3x+2)/((x+1)(x-3))=(x^2+2x+x+2)/((x+1)(x-3))=(x(x+2)+1(x+2))/((x+1)(x-3))\\\\=((x+2)(x+1))/((x+1)(x-3))\qquad\text{cancel (x + 1)}\\\\=(x+2)/(x-3)`