What is 3/(sqrt(15)-3) ?

The solution to 3/(sqrt(15)-3) is (sqrt(15)+3)/2

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simplify 3/(sqrt(15)-3)

simplify

\frac{3}{15 - 3}

\frac{15 + 3}{2}

Decimal Notation

3.43649 \dots

Solution steps

\frac{3}{15 - 3}

Multiply by the conjugate

\frac{15 + 3}{15 + 3}

= \frac{3 ( 15 + 3 )}{( 15 - 3 ) ( 15 + 3 )}

Expand

3 (15 + 3) : 315 + 9

Expand

(15 - 3) (15 + 3) : 6

= \frac{3 15 + 9}{6}

Factor out common term

3 : 3 (15 + 3)

= \frac{3 ( 15 + 3 )}{6}

Factor the number:

6 = 3 \cdot 2

= \frac{3 ( 15 + 3 )}{3 \cdot 2}

Cancel the common factor:

3

= \frac{15 + 3}{2}

\frac{3 ^{4}}{3 ^{7}}

8 x + 12 - 6 (x + 1) - 12

\frac{( 2 a ^{2} ) ^{3}}{b}

\frac{7}{8} \div \frac{14}{9}

(x + 1) (x - 2) + 3 y (x - 2)