What is the numerical value of the simplified expression \frac{4}{\sqrt{5} - 1} - \sqrt{5}… — JAMB UTME

What is the numerical value of the simplified expression $\frac{4}{\sqrt{5} - 1} - \sqrt{5}$ ?

Answer: 1

The numerical value of the expression is 1.

Multiplying the top and bottom of

\frac{4}{\sqrt{5} - 1}

by its conjugate

(\sqrt{5} + 1)

simplifies the fraction to

\frac{4(\sqrt{5} + 1)}{4} = \sqrt{5} + 1

. Subtracting

\sqrt{5}

from

\sqrt{5} + 1

leaves 1.

Rationalize the denominator of the fractional term

\sqrt{5} + 1

Multiply both numerator and denominator by the conjugate

(\sqrt{5} + 1)

to apply the difference of two squares identity

(a-b)(a+b) = a^2 - b^2

in the denominator.

Subtract the remaining surd term

Subtract

\sqrt{5}

from

\sqrt{5} + 1

, leaving the integer 1.

Rationalization of Binomial Denominators

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