Question

√x+4+√x−10/√x+4−√x−10=5/2

Answer 1

Step-by-step explanation:

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

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

$- x - 10 \sqrt{x} - 4 \sqrt{x} - 40 + x + 4 \sqrt{x} - 10 \sqrt{x} - 40 = \frac{5}{2} ( \sqrt{x} ( - \sqrt{x} - 10) + 4( - \sqrt{x} - 10)$

$- 20 \sqrt{x} = \frac{5}{2} ( - x - 10 \sqrt{x} ) - 4 \sqrt{x} + 40)$

$- 40 \sqrt{x} = 5( - x - 10 \sqrt{x} - 4 \sqrt{x} + 40$

$- 40 \sqrt{x} = 5( - x - 14 \sqrt{x} + 40)$

$- 40 \sqrt{x } = - 5x - 70 \sqrt{x} + 200$

$- 40 \sqrt{x} + 5x + 70 \sqrt{x} - 200 = 0$

$5x + 30 \sqrt{x} - 200 = 0$

$x + 6 \sqrt{x} - 40=0 \: i s \: the \: \: answer \: of \: this \: question$

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