Express 3 - [$\frac{x - y}{y}$] as a single fraction

Analyze the question: We need to write 3 − (x − y)/y as one fraction. The key is to give 3 the same denominator, y, as the other term.

Concept: To combine a whole number and a fraction, write the whole number as a fraction with the same denominator: 3 = 3y/y

Solution:

3 − (x − y)/y = 3y/y − (x − y)/y = [3y − (x − y)]/y

Be careful with the minus sign in front of the bracket. It changes the sign of both terms inside:

= (3y − x + y)/y = (4y − x)/y

Check with numbers: Let x = 5 and y = 2.

• Original: 3 − (5 − 2)/2 = 3 − 1.5 = 1.5
• Option C: (4·2 − 5)/2 = 3/2 = 1.5 ✓
• Option B: (5 − 8)/2 = −1.5 ✗

Answer: C. (4y − x)/y

Tip: When you subtract a fraction whose numerator has more than one term, put that numerator in brackets first. Forgetting to distribute the minus sign (getting 3y − x − y) is the most common mistake here, and option B is the trap for it. Option B is actually (x − 4y)/y, which is the negative of the correct answer.