1. make p the subject:
p/p-3= R
2. make R the subject
a= 1- 1/R
You must mean
p/(p-3) = R
cross-multiply
Rp - 3R = p
Rp - p = 3R
p(R-1) = 3R
p = 3R/(R-1)
for the second, multiply each term by R, rearrange and factor in a similar way.
Let me know what you get.
So for the second one, I multiplied each term by R
aR= R- 1
but then I got stuck after that... sorry
you are looking for R, so get the R's to one side
aR - R = -1
factor out the R
R(a-1) = -1
divide both sides by a-1
R = -1/(a-1)
To make p the subject in the equation p/(p-3) = R, we need to isolate p on one side of the equation. Here's how you can do it step-by-step:
1. Multiply both sides of the equation by (p-3) to eliminate the denominator:
(p/p-3) * (p-3) = R * (p-3)
This simplifies to:
p = R * (p-3)
2. Expand the right side of the equation by distributing R:
p = R * p - 3R
3. Move all terms with p to one side of the equation:
p - R * p = -3R
4. Factor out p on the left side:
p * (1 - R) = -3R
5. Lastly, divide both sides of the equation by (1 - R) to solve for p:
p = -3R / (1 - R)
Therefore, the value of p, when solving for p as the subject, is -3R / (1 - R).
Now, for the second equation:
To make R the subject in the equation a = 1 - 1/R, follow these steps:
1. Subtract a from both sides of the equation:
a - 1 = -1/R
2. Take the reciprocal of both sides of the equation:
1 / (a - 1) = R / -1
3. Simplify the expression on the right side:
1 / (a - 1) = -R
4. Multiply both sides of the equation by -1 to solve for R:
-R = 1 / (a - 1)
5. Finally, divide both sides of the equation by -1 to get R by itself:
R = -1 / (a - 1)
Therefore, the value of R, when solving for R as the subject, is -1 / (a - 1).