If a/b=1/3 then (3a+2b)/(3a-2b)is equal to

Options

A. 3
B. (-3)
C. (-5)
D. (-1)

Answer

To solve the problem, we start with the given equation:

\[ \frac{a}{b} = \frac{1}{3} \]

From this, we can express \(a\) in terms of \(b\):

\[ a = \frac{1}{3}b \]

Now we need to evaluate the expression:

\[ \frac{3a + 2b}{3a - 2b} \]

**Step 1: Substitute \(a\) in the expression.**

Substituting \(a = \frac{1}{3}b\) into the expression:

\[ 3a = 3 \left(\frac{1}{3}b\right) = b \]

So, we can rewrite the expression as:

\[ \frac{b + 2b}{b - 2b} \]

**Step 2: Simplify the numerator and denominator.**

Now simplify the numerator and denominator:

Numerator:
\[ b + 2b = 3b \]

Denominator:
\[ b - 2b = -b \]

So the expression now becomes:

\[ \frac{3b}{-b} \]

**Step 3: Simplify the fraction.**

Now we can simplify this fraction:

\[ \frac{3b}{-b} = -3 \]

Thus, the final result is:

\[ \frac{3a + 2b}{3a - 2b} = -3 \]

### Final Answer:
\[ -3 \]

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