Question

factorise 3 by X + 1 - 1 by 2 equal to 2 by 3 x minus 1 where X is not equal to -1 and 1 by 3​

Answer 1

Solution :

$\implies \tt \frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3x - 1}\\\\\tt \implies \frac{6 - (x + 1)}{2(x + 1)} = \frac{2}{3x - 1} \\ \\ \tt \implies \frac{5 - x}{2x + 2} = \frac{2}{3x - 1} \\ \\ \bf \:By \: cross \: multiply \\ \\ \tt \implies(5 - x)(3x - 1) = 2(2x + 2) \\ \\ \tt \implies15x - 5 - 3 {x}^{2} + x = 4x +4 \\ \\\tt \implies - 3 {x}^{2}+ 15x + x - 4x - 5 - 4 = 0 \\ \\ \tt \implies - 3 {x}^{2} + 12x - 9 = 0 \\ \\\tt \implies 3 {x}^{2} - 12 + 9 = 0 \\ \\ \bf By \: splitting \: midde \:term \\ \\ \tt \implies3 {x}^{2} - 9 x - 3x + 9 = 0 \\ \\ \tt \implies3x(x - 3) - 3(x - 3) = 0 \\ \\ \tt \implies(3x - 3)(x - 3) = 0 \\ \\ \tt \implies x =1 \: \: \: \: \: \: \: \: \: \: \: \implies x = 3$

Answer 2

Answer:

-1/3 ❤️❤️❤️❤️❤️