Question

2x/x-4 + 2x-5/x-3 = 25/3

Answer 1

${\bold{\huge{\underline{\green{Answer:}}}}}$

$\large\sf\implies{\dfrac{2x}{x-4}}+{\dfrac{2x-5}{x-3}}=\dfrac{25}{3}$

$\large\sf\implies\dfrac{2x(x-3)+(2x-5)(x-4)}{(x-4)(x-3)}=\dfrac{25}{3}$

$\large\sf\implies\dfrac{(2x^2-6x)+(2x^2-5x-8x+20)}{(x^2-3x-4x+12)}=\dfrac{25}{3}$

$<b><u>Rearrange in order:$

$\large\sf\implies\dfrac{4x^2-19x+20}{x^2-7x+12}=\dfrac{25}{3}$

$<b><u> cross multiplication:$

$\large\sf\implies\:3\:(\:4x^2-19x+20)=25\:(x^2-7x+12)$

$\large\sf\implies\:12x^2-57x+60=25x^2-175x+300$

$\large\sf\implies\:25x^2-12x^2-175x+57x+300-60=0$

$\large\sf\implies\:{13x^2-118x+240=0}$

$\large\textsf{By quadratic equation you will get answer}$

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