((14x^2 +16)/(21))−((2x^2 +8)/(8x^2 −11))=((2x^2 )/3)


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Question Number 35338 by jasno91 last updated on 18/May/18

$\frac{14 x^{2} + 16}{21} - \frac{2 x^{2} + 8}{8 x^{2} - 11} = \frac{2 x^{2}}{3}$
Commented by Rasheed.Sindhi last updated on 18/May/18

$Let x^{2} = y$ $\frac{14 y + 16}{21} - \frac{2 y + 8}{8 y - 11} = \frac{2 y}{3}$ $(14 y + 16) (8 y - 11) - 21 (2 y + 8) = 14 y (8 y - 11)$ $\overset{\times}{112 y^{2}} \overset{\times}{- 154 y} + 128 y - 176 = \overset{\times}{112 y^{2}} \overset{\times}{- 154 y}$ $128 y - 176 = 0$ $y = \frac{176}{128} = \frac{11}{8}$ $x^{2} = \frac{11}{8}$ $x = \pm \sqrt{\frac{11}{8}} = \frac{\pm \sqrt{11}}{2 \sqrt{2}}$
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