write in simplified radical form by rationalizing the denominator 2�ã5 + 3/�ã5 - 1

is this the equation ?,

2(sqrt5) + 3/(sqrt5) - 1

2(sqrt5) + 3(sqrt5)/5 - 1

to get rid of the radical in 3/(sqrt5).
multiply 3/(sqrt5)*sqrt5/sqrt5 = 3(sqrt5)/5

-6/8 - 6/8 =

To write the expression (2√5 + 3) / (√5 - 1) in simplified radical form by rationalizing the denominator, you can follow these steps:

Step 1: Multiply both the numerator and denominator by the conjugate of the denominator. The conjugate is formed by changing the sign of the second term in the denominator. In this case, the conjugate is (√5 + 1).

(2√5 + 3) / (√5 - 1) * (√5 + 1) / (√5 + 1)

Step 2: Simplify the expression by using the distributive property.

[(2√5 + 3)(√5 + 1)] / [(√5 - 1)(√5 + 1)]

Step 3: Apply the FOIL method (First, Outer, Inner, Last) to expand the numerator and the denominator.

[2√5 * √5 + 2√5 * 1 + 3 * √5 + 3 * 1] / [√5 * √5 - √5 * 1 + √5 * 1 - 1 * 1]

Simplified:

[2√5 + 2√5 + 3√5 + 3] / [5 - 1]

Step 4: Combine like terms in the numerator.

[4√5 + 3√5 + 3] / 4

Step 5: Add or subtract coefficients in the numerator.

[7√5 + 3] / 4

Therefore, the expression (2√5 + 3) / (√5 - 1) in simplified radical form, rationalizing the denominator, is (7√5 + 3) / 4.