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JAMB Mathematics 2024 Paper

Question : 20

Total: 50

Simplify

\frac{5 + \sqrt{7}}{3 + \sqrt{7}}

Solution:

Concept:

Rationalise the denominator by multiplying by the conjugate of the denominator.

Explanation:

Start with

\frac{5 + \sqrt{7}}{3 + \sqrt{7}}

The conjugate of

3 + \sqrt{7}

3 - \sqrt{7}

Multiply both numerator and denominator by

3 - \sqrt{7}

\frac{5 + \sqrt{7}}{3 + \sqrt{7}} \times \frac{3 - \sqrt{7}}{3 - \sqrt{7}}

Expand the numerator:

(5 + \sqrt{7})(3 - \sqrt{7}) = 15 - 5\sqrt{7} + 3\sqrt{7} - 7

This simplifies to

8 - 2\sqrt{7}

Expand the denominator:

(3 + \sqrt{7})(3 - \sqrt{7}) = 3^2 - (\sqrt{7})^2 = 9 - 7 = 2

So the expression becomes:

\frac{8 - 2\sqrt{7}}{2} = 4 - \sqrt{7}

Thus, the simplified form is

4 - \sqrt{7}

Answer:

4 - \sqrt{7}

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