Will someone please work out this math problem, showing the steps? r^-9 + r^-8 = ?

Question

I am reviewing my math from last semester before the new semester starts. I just need to confirm a few problems... thank you so much!!!

Also, if you have time...

Solve R = rs/r + s = for r.

This one ^ is driving me nuts, and I know it's probably so simple!!!

Answer 1

Just to show that there is another way to look at it...



The greatest common divisor of r^(-9) and r^(-8) is r^(-9) since -9 is the smaller of {-9, -8}.



So factor out r^(-9):



r^-9 + r^-8 = r^(-9) ( 1 + r) = (1 + r) / r^9





I'm pretty sure R = rs/r + s is not what you wanted to say. Because it reduces to

R = s + s = 2s and there is no longer an r to solve for.



As far as multiplying both sides by r goes... Since r occurs in the denominator of rs/r, then we have to assume that r is not equal to 0. Making that assumption we end up with

rR = rs + rs

r(R - 2s) = 0



Since r is not equal to 0, we can multiply both sides by 1/r and we get



R - 2s = 0



R = 2s.



So we conclude that R = 2s and r can be any number except 0.

Answer 2

r^-9 + r^-8 = 1/r^9 +1/r^8 = (r^8 + r^9)/r^17 (nice solution by fcas)



R = rs/r + s = s + s = 2s. Not solvable for r, which can have any value



Another way is to multiply across by r.......



rR = rs + rs = 2rs



r(R -2s) = 0



r = 0; any value



Are you sure you wrote this correctly? If it is r = rs/r + s, then r = 2s

Answer 3

r^-9 + r^-8 =

1/r^9 + 1/r^8 =

1/r^9 + (r/r)(1/r^8) =

1/r^9 + r/r^9 =

(1 + r) / r^9

Answer 4

a million: (t + 4)(r + a million)(t - 2) = (t * r + t * a million + 4 * r + 4 * a million) *(t - 2) = (tr + t + 4r + 4) * (t - 2) = tr * t + tr * -2 + t * t + t * -2 + 4r * t + 4r * -2 + 4 * t + 4 * -2 = t^2r - 2tr + t^2 - 2t + 4tr - 8r + 4t - 8 = rt^2 + t^2 + 2tr + 2t - 8r - 8 2: (r + 6)^2 = (r + 6)*(r + 6) = r * r + r * 6 + 6 *r + 6 * 6 = r^2 + 6r + 6r + 36 = r^2 + 12r + 36 3: (3x - 4)^2 = (3x - 4)*(3x - 4) = 3x * 3x + 3x * -4 + (-4 * 3x) + (-4 * -4) = 9x^2 -12x - 12x + sixteen = 9x^2 - 24x + sixteen 4: (x - 3)(x +3) = x * x + x * 3 + (-3 * x) + (-3 * 3) = x^2 + 3x - 3x - 9 = x^2 - 9

Answer 5

a) (1+r)/r^9

b) R = s