SOLVE FOR P, Q, &R
p + 1/(Q+ 1/R)= 25
To solve for P, Q, and R in the equation p + 1/(Q + 1/R) = 25, we need to isolate each variable.
Step 1: Get rid of the fraction
Multiply both sides of the equation by Q + 1/R to eliminate the denominator:
(Q + 1/R) * (p + 1/(Q + 1/R)) = 25 * (Q + 1/R)
Be careful with the parentheses.
After multiplying and simplifying, the equation becomes:
p(Q + 1/R) + 1 = 25(Q + 1/R)
Step 2: Expand the equation
Distribute p and 25 to the terms inside the parentheses:
pQ + p(1/R) + 1 = 25Q + 25(1/R)
Step 3: Simplify the equation
Combine like terms on both sides of the equation:
pQ + p/R + 1 = 25Q + 25/R
Step 4: Isolate p
Move all terms containing p to one side of the equation:
pQ + p/R - 25Q = 25/R - 1
p(Q + 1/R) - 25Q = 25/R - 1
Factor out p:
p(Q + 1/R - 25) = 25/R - 1
Divide both sides by (Q + 1/R - 25) to solve for p:
p = (25/R - 1) / (Q + 1/R - 25)
This expression gives the value of p in terms of Q and R.