If `m=(cab)/(a-b)` then b equals

Options

A. `(m(a-b))/(ca)`
B. `(cab-ma)/(-m)`
C. `(1)/(1+c)`
D. `(ma)/(m+ca)`

Answer

To solve the equation \( m = \frac{cab}{a - b} \) for \( b \), we can follow these steps:

### Step 1: Write down the given equation
We start with the equation:
\[ m = \frac{cab}{a - b} \]

### Step 2: Cross-multiply
To eliminate the fraction, we cross-multiply:
\[ m(a - b) = cab \]

### Step 3: Expand the left side
Expanding the left side gives us:
\[ ma - mb = cab \]

### Step 4: Rearrange the equation
Now, we want to isolate the terms involving \( b \). We can rearrange the equation:
\[ ma = cab + mb \]

### Step 5: Factor out \( b \)
Next, we can factor \( b \) out from the right side:
\[ ma = b(ca + m) \]

### Step 6: Solve for \( b \)
To find \( b \), we divide both sides by \( (ca + m) \):
\[ b = \frac{ma}{ca + m} \]

### Final Answer
Thus, the value of \( b \) is:
\[ b = \frac{ma}{ca + m} \]

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