2025 · Q14
If (p+q)/(q+r) = (r+s)/(s+p), where denominators are non-zero, then which one of the following is correct?
Elementary MathematicsAlgebra
- Ap=q
- Bq=r
- CEither p=r or p+q+r+s=0
- Dp+q=r+s
Explanation
Cross-multiplying (p+q)(s+p)=(r+s)(q+r) and expanding: ps+p^2+qs+pq=rq+r^2+sq+rs. Rearranging gives (p-r)(p+q+r+s)=0. Hence either p=r or p+q+r+s=0. Assuming p=q (or similar) without doing the algebra is the trap.