Question

solve for x. plz rotate the pic to see the full question the first answer will be marked as brainlist.​

Answer 1

$\huge \boxed{ \colorbox{lime}{ \red{x = - 1}}}$

Step-by-step explanation:

$\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 3 \\ \\ = > \frac{(x + 1)(x + 2) + (x -1)(x - 2)}{(x - 1)(x + 2)} = 3 \\ \\ = > \frac{x(x + 2) + 1(x + 2) + x(x - 2) - 1(x - 2)}{x(x + 2) - 1(x + 2)} = 3 \\ \\ = > \frac{ {x}^{2} + 2x + x + 2 + {x}^{2} - 2x - x + 2 }{ {x}^{2} + 2x - x - 2 } = 3 \\ \\ = > \frac{ {x}^{2} + {x}^{2} + 2x + x - 2x - x + 2 + 2 }{ {x}^{2} + x - 2} = 3 \\ \\ = > 2 {x}^{2} + 3x - 3x + 4 = 3( {x}^{2} + x - 2) \\ \\ = > {2x}^{2} + 4 = 3 {x}^{2} + 3x - 6 \\ \\ = > 4 = { 3x}^{2} - {2x}^{2} + 3x + 6 \\ \\ = > {x}^{2} + 3x + 6 = 4 \\ \\ = > {x}^{2} + 3x + 6 - 4 = 0 \\ \\ = > {x}^{2} + 3x + 2 = 0 \\ \\ = > {x}^{2} + 2x + x + 2 = 0 \\ \\ = > x(x + 2) + 1(x + 2) = 0 \\ \\ = > (x + 2)(x + 1) = 0$

Hence value of x,

value 1 -

x + 1 = 0

=> x = -1

value 2 -

x + 2 = 0

=> x = -2

Hence the value of x = -1, - 2

You've said that we shouldn't take the value of x as 1 and -2.

So we can say the value as -1.

hope it helps.