Question

please answer this question fast​

Answer 1

Answer

x = 1 , x = 6

Explanation

$\rm 2\bigg(\dfrac{2x+3}{x-3}\bigg)-25\bigg( \dfrac{x-3}{2x+3}\bigg)=5$

$\boxed{\begin{minipage}{3.5cm} \\ \rm Let\ ,y=\dfrac{2x+3}{x-3}...(1)\\\\\rightarrow \rm \dfrac{1}{y}=\dfrac{x-3}{2x+3} \\ \end{minipage}}$

$\implies \rm 2(y)-25\bigg(\dfrac{1}{y}\bigg)=5\\\\\implies \rm 2y-\dfrac{25}{y}=5\\\\\implies \rm \dfrac{2y^2-25}{y}=5\\\\\implies \rm 2y^2-25=5y\\\\\implies \rm 2y^2-5y-25=0 \\\\\implies \rm 2y^2-10y+5y-25=0\\\\\implies \rm 2y(y-5)+5(y-5)=0\\\\\implies \rm (y-5)(2y+5)=0\\\\\implies \rm y=5\ \& \; 2y=-5\\\\\implies \rm y=5\ \& \; y=-\dfrac{5}{2}$

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$\rm 5=\dfrac{2x+3}{x-3}\ [From\ (1)]\\\\\implies \rm 5(x-3)=2x+3\\\\\implies \rm 5x-15=2x+3\\\\\implies \rm 5x-2x=3+15\\\\\implies \rm 3x=18\\\\\implies \underline{ \bf x=6}$

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$\rm -\dfrac{5}{2}=\dfrac{2x+3}{x-3}\ [From\ (1)]\\\\\implies \rm -5(x-3)=2(2x+3)\\\\\implies \rm -5x+15=4x+6\\\\\implies \rm 15-6=4x+5x\\\\\implies \rm 9=9x\\\\\implies \underline{ \bf x=1}$

Answer 2

$\large{\red{\underline{\underline{\bold{Given:-}}}}}$

• $\sf 2 \bigg(\dfrac{2x + 3}{x - 3} \bigg) - 25 \bigg( \dfrac{x - 3}{2x + 3} \bigg) = 5$

$\large{\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The value of x.

$\large{\green{\underline{\underline{\bold{Solution:-}}}}}$

$\sf let \: \dfrac{2x + 3}{x - 3} = y$

$\sf \: \dfrac{x - 3}{2x + 3} = \dfrac{1}{y}$

Then:-

$\sf 2y - \dfrac{25}{y} = 5$

$\sf \implies \dfrac{2 {y}^{2} - 25}{y} = 5$

$\sf \implies {2 {y}^{2} - 25} = 5y$

$\sf \implies {2 {y}^{2} - 5y - 25} =0$

$\sf \implies {2 {y}^{2} - 10y + 5y - 25} =0$

$\sf \implies {2 {y}(y - 5) + 5(y - 5)} =0$

$\sf \implies (2y + 5)(y - 5) = 0$

$\sf \implies y = \dfrac{ - 5}{2} \: \: \: (or) \: \: \: y = 5$

____________________

$\sf \implies y = \bigg( \dfrac{2x + 3}{x - 3} \bigg) = 5$

$\sf \implies \dfrac{2x + 3}{x - 3} = 5$

$\sf \implies {2x + 3} = 5({x - 3} )$

$\sf \implies {2x + 3} = 5x - 15$

$\sf \implies 5x - 2x = 15 + 3$

$\sf \implies 3x = 18$

$\sf \implies x = 6$

________________

$\sf \implies \dfrac{1}{y} = \bigg( \dfrac{x - 3}{2x + 3} \bigg) = \dfrac{ - 5}{2}$

$\sf \implies \dfrac{2x + 3}{x - 3} = \dfrac{ - 5}{2}$

$\sf \implies {2(2x + 3)} = - 5({x - 3} )$

$\sf \implies 4x + 6 = - 5x - 15$

$\sf \implies 5x + 4x = 15 - 6$

$\sf \implies 9x = 9$

$\sf \implies x = 1$