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2015-04-19T16:25:25+05:30

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 \frac{ x^{2} -2-3x+ x^{2} -4-5x}{x} =  \frac{10}{3}

 \frac{2 x^{2} -8x-6}{x} =  \frac{10}{3}

6 x^{2} -24x-18=10x

6 x^{2} -34x-18=0          (divide by 2)

 3x^{2}-17x-9=0

Quadratic formula:
= \frac{-b p/m  \sqrt{ b^{2}-4ac } }{2a}

= \frac{17 p/m  \sqrt{ 17^{2}-(4)(3)(-9) } }{2(3)}

= \frac{17 p/m \sqrt{289+108} }{6}

= \frac{17 p/m \sqrt{397} }{6}

= \frac{17 p/m19.925}{6}

x =  \frac{17+19.925}{6} = 6.1541

x =  \frac{17-19.925}{6} -0.4875
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2015-04-19T18:23:09+05:30

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
 \frac{x-2}{x-3} + \frac{x-4}{x-5}= \frac{10}{3} \\ \\ \Rightarrow  \frac{(x-2)(x-5)+(x-4)(x-3)}{(x-3)(x-5)}= \frac{10}{3} \\ \\ \Rightarrow  \frac{(x^2-7x+10)+(x^2-7x+12)}{x^2-8x+15}= \frac{10}{3} \\ \\ \Rightarrow \frac{2x^2-14x+22}{x^2-8x+15}= \frac{10}{3} \\ \\ \Rightarrow 3(2x^2-14x+22)=10(x^2-8x+15)  \\ \\ \Rightarrow 6x^2-42x+66=10x^2-80x+150

\Rightarrow 6x^2-10x^2-42x+80x+66-150=0 \\ \\ \Rightarrow -4x^2+38x-84=0\\ \\ \Rightarrow 4x^2-38x+84=0\\ \\ \Rightarrow 2x^2-19x+42=0\\ \\ \Rightarrow 2x^2-7x-12x+42=0\\ \\ \Rightarrow x(2x-7)-6(2x-7)=0\\ \\ \Rightarrow (2x-7)(x-6)=0\\ \\ \Rightarrow 2x=7\ or\ x=6\\ \\ \Rightarrow x=\boxed{ \frac{7}{2}} \ or\ x=\boxed{6}
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