Chisom A. answered • 2d

College & High School Math Tutor

(√5 + 3)/(√5 - 3)

Multiply the numerator and denominator by the conjugate of the denominator: (√5 + 3)

= (√5 + 3)/(√5 - 3) * (√5 + 3)/(√5 + 3)

= (√5 + 3)^{2 }/ [(√5 - 3)*(√5 + 3)]

For the denominator, difference of two squares: (a - b)(a + b) = a^{2} - b^{2}

= [(√5)^{2 }+ 2(3)(√5) + 3^{2}] / [(√5)^{2} - 3^{2}]

= (5 + 6√5 + 9) / (5 - 9)

= (14 + 6√5) / (-4)

= (-14/4) + (-6√5 / 4)

= -7/2 - (3/2)*√5

The **fourth** option would be the correct answer.