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

The solution to 4/(7-sqrt(5)) is (7+sqrt(5))/(11)

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simplify 4/(7-sqrt(5))

simplify

\frac{4}{7 - 5}

\frac{7 + 5}{11}

Solution steps

\frac{4}{7 - 5}

Multiply by the conjugate

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

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

Expand

4 (7 + 5) : 28 + 45

Expand

(7 - 5) (7 + 5) : 44

= \frac{28 + 4 5}{44}

Factor out common term

4 : 4 (7 + 5)

= \frac{4 ( 7 + 5 )}{44}

Factor the number:

44 = 4 \cdot 11

= \frac{4 ( 7 + 5 )}{4 \cdot 11}

Cancel the common factor:

4

= \frac{7 + 5}{11}

\frac{3 y + \frac{4}{y + 1}}{2 y - \frac{3}{y}}

5 + \frac{1}{75} (x - 125)

2^{5} \cdot 3^{2} \cdot 5^{2}

\frac{3}{4} + \frac{4}{8}

- \frac{1}{4} + \frac{5}{4}