Divide: (sqrt(5) + 3) / (sqrt(5) - 3)

Question

Divide by multiplying the denominator by its conjugate, then simplify. If your answer doesn't match any of these answers, see how you can rewrite your expression to equal one of these. Divide: (sqrt(5) + 3) / (sqrt(5) - 3)

7/2 - (3/2) sqrt(5)

7/2 + (3/2) sqrt(5)

1 - (3/2) sqrt(5)

-7/2 - (3/2) sqrt(5)

-17/2+(3/2) sqrt(5)

Answer 1

(√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) = a² - b²

= [(√5)² + 2(3)(√5) + 3²] / [(√5)² - 3²]

= (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.

Answer 2

Multiply both numerator and denominator by the conjugate of the denominator.

sqrt(5)+3 is the conjugate. Just change the sign of -3 to +3

The new denominator is 5-9=-4.

The numerator is now 5 +6sqrt(5)+9 = 14+6sqrt(5) Divide that by -4 to get

-14/4-6sqrt(5)/4 = -7/2 - (3/2)sqrt(5) that's the 2nd to last answer in your list of answers