Algebra help i can't figure out how to solve this equation?

Question

i already asked my mom but she never took algebra 2 & i'm homeschooled so please just show me the steps to solve it (its probably simple & i might know how but i'm just confused)



Peter says that the following equations are two ways to write the SAME formula. Solve them both for the same variable to decide whether or not you agree with Peter. Explain how you made your decision, based on solving for variables.

p = (r - 1)/r
(p equals r minus 1 over r)

p = r/(p + 1)
(p equals r over p plus 1)

thanks so much!

Answer 1

We'll solve both for r.
First problem - you can rewrite the fraction as two separate fractions.
p = r/r - 1/r
p=1 - 1/r
p-1 = -1/r
r = -1/(p-1)
Second problem - cross multiply
r = p(p+1)

You can plug in a number for p and see these are clearly not the same.

Answer 2

Suppose in the first equation r=2. Then p=(2-1)/2=1/2

OK, so put p=1/2 in the second euqation and see what happens.
1/2 = r /(1/2 +1)
so 1/2 = r / (3/2)
so r = 3/4

so clearly they aren't the same.

Answer 3

p = r/(p + 1)
p^2 +p = r
p^2+p +1/4 = r+1/4
(p+.5)^2 = r+ 1/4
p + .5 = +/- sqrt(r+.25)
p = -.5 +/- sqrt(r+.25)

This is not = (r-1)/r

Answer 4

wow i did algebra lyk last year but i don seem 2 remember if i did this or not id thynk so so srry i waz in gifted nd we never really did algebra it waz kinda lyk sumthyin we did cuz we did pre algebra a year b 4 so it waz 4 "FUN"

Answer 5

those arent the same, its impossible to get that