Question

I need to find the sum of this equation

Answer 1

`\large\boxed{(3s^2+19s-4)/((s-1)^2(s+5))=(3s^2+19s-4)/(s^3+3s^2-9s+5)}`

Explanation:

`s^2-2s+1=s^2-s-s+1=s(s-1)-1(s-1)=(s-1)(s-1)=(s-1)^2\\\\s^2+4s-5=s^2+5s-s-5=s(s+5)-1(s+5)=(s+5)(s-1)\\\\\text{Therefore}\ LCD\ \text{is}\ (s-1)^2(s+5).`

`(3s)/(s^2-2s+1)+(4)/(s^2+4s-5)=(3s(s+5))/((s-1)^2(s+5))+(4(s-1))/((s-1)^2(s+5))\\\\\text{use the distributive property}\\\\=((3s)(s)+(3s)(5)+(4)(s)+(4)(-1))/((s-1)^2+(s+5))=(3s^2+15s+4s-4)/((s-1)^2(s+5))\\\\=(3s^2+19s-4)/((s-1)^2(s+5))`