If `(b+a)/(b-a)=11/5`, find the value of `a/b`.

Options

A. 7
B. `15/7`
C. `3/8`
D. `8/3`

Answer

To solve the equation \(\frac{b+a}{b-a} = \frac{11}{5}\) and find the value of \(\frac{a}{b}\), we can follow these steps:

### Step 1: Cross Multiply
We start by cross multiplying the given equation:
\[ 5(b + a) = 11(b - a) \]

### Step 2: Distribute
Now, we distribute both sides:
\[ 5b + 5a = 11b - 11a \]

### Step 3: Move Terms Involving \(a\) to One Side
Next, we will move all terms involving \(a\) to one side and all terms involving \(b\) to the other side:
\[ 5a + 11a = 11b - 5b \]
This simplifies to:
\[ 16a = 6b \]

### Step 4: Simplify the Equation
Now, we can simplify this equation to find the ratio \(\frac{a}{b}\):
\[ \frac{a}{b} = \frac{6}{16} \]
This can be further simplified:
\[ \frac{a}{b} = \frac{3}{8} \]

### Final Answer
Thus, the value of \(\frac{a}{b}\) is:
\[ \frac{3}{8} \]

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