Question

solve 2/(x+1) + 3/2(x-2) = 23/5x​

Answer 1

$\dashrightarrow \sf \dfrac{2}{(x + 1)} + \dfrac{3}{2(x - 2)} = \dfrac{23}{5x}$

$\dashrightarrow \sf \dfrac{4(x - 2) + 3(x + 1)}{2(x - 2)(x + 1)} = \dfrac{23}{5x}$

$\dashrightarrow \sf \dfrac{4x - 8 + 3x + 3}{2( {x}^{2} - x - 2)} = \dfrac{23}{5x}$

$\dashrightarrow \sf \dfrac{7x - 5}{2( {x}^{2} - x - 2)} = \dfrac{23}{5x}$

$\dashrightarrow \sf 5x(7x - 5)= 46({x}^{2} - x - 2)$

$\dashrightarrow \sf {35x}^{2} - 25x = 46 {x}^{2} - 46x - 92$

$\dashrightarrow \sf {11x}^{2} - 21x - 92 = 0$

by splitting the middle terms,

$\dashrightarrow \sf {11x}^{2} - 44x + 23x - 92 = 0$

$\dashrightarrow \sf 11x(x - 4) + 23(x - 4) = 0$

$\dashrightarrow \sf (11x + 23)(x - 4) = 0$

$\dashrightarrow \sf 11x + 23 = 0 \: and \: x - 4 = 0$

$\dashrightarrow \sf x = \dfrac{ - 23}{ \: 11} \: and \: x = 4$

Hence, x = -23/11 or 4

Answer 2

here's your answer

hope it helped