WAEC Further Mathematics 2012 Paper

Step 1: Simplify the denominatorStart by simplifying the denominator. First, note that $(x^{2n-3})^{\;\frac{1}{2}} = x^{\;\frac{2n-3}{2}}$. Thus, the denominator becomes:$x^{2n+\;\frac{5}{2}} \cdot x^{\;\frac{2n-3}{2}}$Now, use the property of exponents that $x^a \cdot x^b = x^{a+b}$. Therefore, the denominator simplifies to:$x^{2n+\;\frac{5}{2}+\;\frac{2n-3}{2}} = x^{2n+\;\frac{5+2n-3}{2}} = x^{2n+\;\frac{2n+2}{2}} = x^{2n+(n+1)} = x^{3n+1}$Step 2: Simplify the entire expressionNow, substitute the simplified denominator back into the original expression:$\frac{\; x^{3n+1}}{x^{3n+1}}$Since the numerator and denominator are the same, the expression simplifies to:1