you're probably confusing signs... try to take 1/r+1 to the ledtside and 1/2 to the right, the factorise 1/r+1 and derive the quadratic equation ...what do you get?
I have the following problem and I've been trying to solve it
but when I try solving I just can't figure out how they get to 3 and -5. I'm supposed to solve it turning it into
I need to get rid of these denominators and therefore multiply the whole expression by its least common denominator
but I stay stucked...!! Need guidance.
Note that (difference of two squares)
This means that the denominator is
Then multiply by 2 to get
The denominator will cancel and then should be easy to simplify and solve - just remember that as this would entail division by 0
Start this way (easier LCM):
6 / (r^2 - 1) = 1 / (r + 1) + 1/2 ; combine right side:
6 / (r^2 - 1) = (r + 3) / [2(r + 1)] ; factor left side:
6 / [(r + 1)(r - 1)] = (r + 3) / [2(r + 1)] ; cancel out the (r + 1)'s:
6 / (r - 1) = (r + 3) / 2 ; crossmultiply:
(r - 1)(r + 3) = 12 ; expand left side:
r^2 + 2r - 3 = 12
Can you wrap it up? I'm sure you can.