What is 4/(5-sqrt(7)) ?

The solution to 4/(5-sqrt(7)) is (2(5+sqrt(7)))/9

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simplify 4/(5-sqrt(7))

simplify

\frac{4}{5 - 7}

\frac{2 ( 5 + 7 )}{9}

Decimal Notation

1.69905 \dots

Solution steps

\frac{4}{5 - 7}

Multiply by the conjugate

\frac{5 + 7}{5 + 7}

= \frac{4 ( 5 + 7 )}{( 5 - 7 ) ( 5 + 7 )}

Expand

4 (5 + 7) : 20 + 47

Expand

(5 - 7) (5 + 7) : 18

= \frac{20 + 4 7}{18}

Factor out common term

4 : 4 (5 + 7)

= \frac{4 ( 5 + 7 )}{18}

Factor the number:

4 = 2 \cdot 2

= \frac{2 \cdot 2 ( 5 + 7 )}{18}

Factor the number:

18 = 2 \cdot 9

= \frac{2 \cdot 2 ( 5 + 7 )}{2 \cdot 9}

Cancel the common factor:

2

= \frac{2 ( 5 + 7 )}{9}

- 2 < 2 - 2 x \leq 10

(10 + 6) (10 - 3)

x^{2} + 7 = - 300

8 - ∣ 5 - 2 x ∣ = 2

\frac{( - 2 ) ^{7}}{( - 2 ) ^{5}}