What is 3/(sqrt(7)-2) ?

The solution to 3/(sqrt(7)-2) is sqrt(7)+2

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simplify 3/(sqrt(7)-2)

simplify

\frac{3}{7 - 2}

7 + 2

Decimal Notation

4.64575 \dots

Solution steps

\frac{3}{7 - 2}

Multiply by the conjugate

\frac{7 + 2}{7 + 2}

= \frac{3 ( 7 + 2 )}{( 7 - 2 ) ( 7 + 2 )}

Expand

3 (7 + 2) : 37 + 6

Expand

(7 - 2) (7 + 2) : 3

= \frac{3 7 + 6}{3}

Factor out common term

3 : 3 (7 + 2)

= \frac{3 ( 7 + 2 )}{3}

Cancel the common factor:

3

= 7 + 2

4 (x + 2)^{2} + 100 = 14

- 2 x^{2} + 38 x - 180

2 k^{3} + 9 k^{2} + 13 k + 6

∣ x - 7 ∣ - 3 \geq 8

\frac{9}{8}