simplify (2-sqrt(3))/(2+sqrt(3))

Let's reduce:

\frac{2 - \sqrt{3}}{2 + \sqrt{3}}

Multiply numerator and denominator by the conjugate

2 - \sqrt{3}

: (a+b)(a-b) = a²-b², here

2^{2} - {(\sqrt{3})}^{2}

4 - 3

1

ⅰ

\frac{2 - \sqrt{3}}{2 + \sqrt{3}}

(2 - \sqrt{3}) \times (2 - \sqrt{3})

(2 - \sqrt{3}) \times (2 - \sqrt{3})

ⓘ Expand by multiplying each term inside the parentheses:

(2 - \sqrt{3}) \times (2 - \sqrt{3})

2 \times 2

+ 2 \times (- \sqrt{3})

- \sqrt{3} \times 2

- \sqrt{3} \times (- \sqrt{3})

2 \times 2

+ 2 \times (- \sqrt{3})

- \sqrt{3} \times 2

- \sqrt{3} \times (- \sqrt{3})

ⓘ Multiplications are done before additions and subtractions:

2 \times 2

4

■The minus sign is placed in front of the product:

2 \times (- \sqrt{3})

- 2 \times \sqrt{3}

■Multiplying powers with the same base adds the exponents:

- \sqrt{3} \times (- \sqrt{3})

3

4

- 2 \times \sqrt{3}

- \sqrt{3} \times 2

+ 3

ⓘ Start from

4

and move forward

3

on the number line:

4 + 3

7

■Like terms are grouped by adding their coefficients:

- 2 \times \sqrt{3} - \sqrt{3} \times 2

-4 \times \sqrt{3}

▶Simplified form:

7 - 4 \times \sqrt{3}

The numeric value of:

7 - 4 \times \sqrt{3}

equals:

7 - 4 \times \approx 1.7321

7 - \approx 6.9282

▷

\approx 7.1797 \times 10^{- 2}