If `(a-b)/(b)=(2)/(3)`, what is the value of `(a)/(b)`?

Options

A. `(1)/(2)`
B. `(3)/(5)`
C. `(3)/(2)`
D. `(5)/(3)`

Answer

To solve the equation \(\frac{a-b}{b} = \frac{2}{3}\) and find the value of \(\frac{a}{b}\), we can follow these steps:

### Step 1: Start with the given equation
We have:
\[ \frac{a-b}{b} = \frac{2}{3} \]

### Step 2: Cross multiply
To eliminate the fractions, we can cross multiply:
\[ 3(a - b) = 2b \]

### Step 3: Distribute on the left side
Distributing \(3\) on the left side gives us:
\[ 3a - 3b = 2b \]

### Step 4: Combine like terms
Next, we can add \(3b\) to both sides to combine the \(b\) terms:
\[ 3a = 2b + 3b \]
This simplifies to:
\[ 3a = 5b \]

### Step 5: Solve for \(\frac{a}{b}\)
Now, we can divide both sides by \(3b\) to isolate \(\frac{a}{b}\):
\[ \frac{a}{b} = \frac{5}{3} \]

### Final Answer
Thus, the value of \(\frac{a}{b}\) is:
\[ \frac{5}{3} \]

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