Question

slove for x
$\sqrt{x - 4} + \sqrt{x - 10 } \div \sqrt{x + 4} - \sqrt{x - 10} = 5 \div 2$
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Answer 1

Answer:

$\frac{ \sqrt{x + 4 } + \sqrt{x - 10} }{ \sqrt{x + 4} - \sqrt{x - 10} } = \frac{5}{2}$

$\frac{ \sqrt{x + 4} + \sqrt{x - 10} }{ \sqrt{x + 4} - \sqrt{x - 10} } \times \frac{ \sqrt{x + 4} + \sqrt{x - 10} }{ \sqrt{x + 4} + \sqrt{x - 10} } = \frac{5}{2}$

$\frac{( \sqrt{x + 4 })^{2} + ( \sqrt{x - 10})^{2} }{( \sqrt{x + 4} )^{2} - ( \sqrt{x - 10})^{2} } = \frac{5}{2}$

$\frac{( \sqrt{x})^{2} + 8 \sqrt{x} + {4}^{2} + ( \sqrt{x})^{2} - 20 \sqrt{x} + 10^{2} }{( \sqrt{x})^{2} +8 \sqrt{x} + {4}^{2} -[( \sqrt{x})^{2} - 20 \sqrt{x} + 10 ^{2}] } = \frac{5}{2}$

$\frac{x + 8 \sqrt{x} + 16 + x - 20 \sqrt{x} + 100}{x + 8 \sqrt{x} + 16 - x + 20 \sqrt{x} - 100} = \frac{5}{2}$

$\frac{2x + 116 - 12 \sqrt{x} }{28 \sqrt{x} - 84 } = \frac{5}{2}$

$squaring \: both \: the \: side$

$( \frac{2x + 116 - 12 \sqrt{x} }{28 \sqrt{x} - 84 } )^{2} = (\frac{5}{2})^{2}$

$\frac{4x + 13,456 - 144x}{784x -7,056} = \frac{25}{4}$

$\frac{13456 - 140x}{784x - 7056} = \frac{25}{4}$

$4(13456 - 140x) = 25(784x - 7056)$

$53,824 - 560x = 19,600x - 176,400$

$- 560x - 19600x = - 176400 - 53824$

$- 20160x = - 122,576$

Answer 2

Answer:

answer = 122567

have your answer........