JAMB Mathematics 1979 Question 21

Question 21

Algebraic Expressions

Simplify (x² + y² + xy)/(x + y) − (x² + y² − xy)/(x − y)

A.(x² + y²)/(x − y)²
B.2x³/x² − y²
C.2y³/(y² − x²)
D.(2x² − 2y²)/(x² + y²)
E.(2x² + 2y²)/(x² − y²)

Show the answer and explanation

Answer: C (2y³/(y² − x²))

Explanation

Over the common denominator x² − y², the top is (x − y)(x² + xy + y²) − (x + y)(x² − xy + y²) = (x³ − y³) − (x³ + y³) = −2y³. So the result is −2y³/(x² − y²) = 2y³/(y² − x²).