If `(1)/(p+q)=r and pne-q`. What is p in terms of r and q?

Options

A. `(rq-1)/(q)`
B. `(1+rq)/(q)`
C. `(r)/(1+rq)`
D. `(1-rq)/(r)`

Answer

To solve the equation \( \frac{1}{p+q} = r \) for \( p \) in terms of \( r \) and \( q \), follow these steps:

### Step 1: Multiply both sides by \( p + q \)
We start with the equation:
\[ \frac{1}{p + q} = r \]
To eliminate the fraction, multiply both sides by \( p + q \):
\[ 1 = r(p + q) \]

### Step 2: Distribute \( r \) on the right side
Now, distribute \( r \) on the right side:
\[ 1 = rp + rq \]

### Step 3: Rearrange the equation to isolate \( rp \)
Next, we want to isolate \( rp \). To do this, subtract \( rq \) from both sides:
\[ 1 - rq = rp \]

### Step 4: Divide both sides by \( r \)
Now, divide both sides by \( r \) to solve for \( p \):
\[ p = \frac{1 - rq}{r} \]

### Final Expression
Thus, we have expressed \( p \) in terms of \( r \) and \( q \):
\[ p = \frac{1 - rq}{r} \]