Rationalize the denominator and simplify: (sqrt (b))/(3+sqrt (b)) (3sqrt (b)-b)/(9-b) (3-b)/(9-b) (2sqrt (b))/(9-b) 1 (1)/(3)

## Step 1: Identify the problem### The goal is to rationalize the denominator of and simplify it step-by-step.## Step 2: Multiply numerator and denominator by the conjugate### To rationalize the denominator, multiply both numerator and denominator by the conjugate of , which is . This eliminates the square root in the denominator: ## Step 3: Simplify the denominator### Use the difference of squares formula: \( (a+b)(a-b) = a^2 - b^2 \). Here, and : ## Step 4: Expand the numerator### Distribute across \( (3-\sqrt{b}) \): ## Step 5: Combine results### Substitute the simplified numerator and denominator back into the fraction: ## Step 6: Verify simplification options### Among the given options, matches the simplified form. No further simplifications are possible.