What is (sqrt(125)-sqrt(7))/(sqrt(35)-5) ?

The solution to (sqrt(125)-sqrt(7))/(sqrt(35)-5) is (10sqrt(7)+9sqrt(5))/5

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simplify (sqrt(125)-sqrt(7))/(sqrt(35)-5)

simplify

\frac{125 - 7}{35 - 5}

\frac{10 7 + 9 5}{5}

Solution steps

\frac{125 - 7}{35 - 5}

125 = 55

= \frac{5 5 - 7}{35 - 5}

Multiply by the conjugate

\frac{35 + 5}{35 + 5}

= \frac{( 5 5 - 7 ) ( 35 + 5 )}{( 35 - 5 ) ( 35 + 5 )}

Expand

(55 - 7) (35 + 5) : 207 + 185

Expand

(35 - 5) (35 + 5) : 10

= \frac{20 7 + 18 5}{10}

Factor out common term

2 : 2 (107 + 95)

= \frac{2 ( 10 7 + 9 5 )}{10}

Factor the number:

10 = 2 \cdot 5

= \frac{2 ( 10 7 + 9 5 )}{2 \cdot 5}

Cancel the common factor:

2

= \frac{10 7 + 9 5}{5}

16 y^{2} x^{2} + 24 y x^{2} + 9 x^{2}

- 8 m - 12 > - 5 (m - 8) - 3 (m - 7)

\frac{5}{6} + \frac{7}{9} \cdot (\frac{4}{3} - \frac{1}{2})

9150

3 x^{2} - 4 y^{2} + x^{2} y^{2} - 12

What is (sqrt(125)-sqrt(7))/(sqrt(35)-5) ?
The solution to (sqrt(125)-sqrt(7))/(sqrt(35)-5) is (10sqrt(7)+9sqrt(5))/5