Simplify 2√7- $\frac{14}{√7} + \frac{7}{√21}$

Step 1: Analyze the question

We need to simplify 2√7 − 14/√7 + 7/√21 by rationalising each denominator and combining like terms.

Step 2: Simplify each term

• 14/√7 = 14√7/7 = 2√7
• 7/√21 = 7√21/21 = √21/3

Step 3: Combine

2√7 − 2√7 + √21/3 = √21/3

The first two terms cancel, leaving only the third term.

Step 4: Match to the options

√21/3 is option C.

Answer: C

Tip: When you see a fraction like k/√n, multiply the top and bottom by √n to rationalise it. Always check whether terms cancel before doing any heavy computation. Here, 2√7 and 14/√7 are equal, so they cancel.