What is (sqrt(3)-3)/(sqrt(5)-3) ?

The solution to (sqrt(3)-3)/(sqrt(5)-3) is -(sqrt(15)+3sqrt(3)-3sqrt(5)-9)/4

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simplify (sqrt(3)-3)/(sqrt(5)-3)

simplify

\frac{3 - 3}{5 - 3}

- \frac{15 + 3 3 - 3 5 - 9}{4}

Decimal Notation

1.65976 \dots

Solution steps

\frac{3 - 3}{5 - 3}

Multiply by the conjugate

\frac{5 + 3}{5 + 3}

= \frac{( 3 - 3 ) ( 5 + 3 )}{( 5 - 3 ) ( 5 + 3 )}

Expand

(3 - 3) (5 + 3) : 15 + 33 - 35 - 9

Expand

(5 - 3) (5 + 3) : - 4

= \frac{15 + 3 3 - 3 5 - 9}{- 4}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{15 + 3 3 - 3 5 - 9}{4}

\frac{3}{5} \div \frac{9}{10}

4 \cdot 45

10 - 19 x - 15 x^{2}

cot^{2} (t) (2 sec^{2} (t) - 2)

(m^{9})^{2}

What is (sqrt(3)-3)/(sqrt(5)-3) ?
The solution to (sqrt(3)-3)/(sqrt(5)-3) is -(sqrt(15)+3sqrt(3)-3sqrt(5)-9)/4