MATHEMATICS

JAMB 2001 - Question 6

Mathematics 2001 JAMB Past Questions - Question 6: If y/2 = x , evaluate (x/y + ½ ) ⁄ (1/2- x²/y²)

If y/2 = x , evaluate (x/y + ½ ) ⁄ (1/2- x²/y²)
A:
B:
C:
D:
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Correct Answer

D

Explanation

To evaluate the expression (x/y + 1/2) / (1/2 - x²/y²), we need to substitute the value of x in terms of y and simplify the expression.Given:y/2 = xLet's substitute this value into the expression:(x/y + 1/2) / (1/2 - x²/y²) = ((y/2)/y + 1/2) / (1/2 - (y/2)²/y²)Simplifying:= ((1/2) + 1/2) / (1/2 - (y/2)²/y²)= (1 + 1) / (1/2 - (y/2)²/y²)= 2 / (1/2 - (y/2)²/y²)To simplify further, let's find a common denominator:= 2 / (1/2 - (y/2)²/y²) * (2y²/2y²)= 2(2y²) / (y² - (y/2)²)= 4y² / (y² - y²/4)= 4y² / (4y²/4 - y²/4)= 4y² / (3y²/4)= (4y² * 4) / (3y²)= 16y² / 3y²= 16/3Therefore, the evaluated expression is 16/3.