Question

find the value of X in x+1÷x-1 +x-2÷x+2=3​

Answer 1

Answer:

$\large \red{ \underline{ \underline{question}}} \\ \implies{ \large{ \frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 3 }} \\ \large{ \underline{to \: find \: the \: value \: of \: x}} \\ \large \orange{ \underline{solution}} \\ \implies{ \large{ \frac{(x + 1)(x + 2) + (x - 1)(x - 2)}{(x - 1)(x + 2)} = 3 }} \\ \implies{ \large{ \frac{ {x}^{2} + 2x + x + 2 + {x}^{2} - 2x - x + 2 }{ {x}^{2} + 2x - x - 2} = 3}} \\ \implies{ \large{ \frac{2 {x}^{2} + 4}{ {x}^{2} + x - 2 } = 3 }} \\ \implies{ \large{ {2 {x }^{2} + 4 = 3 {x}^{2} + 3x - 6 }{} }} \\ \implies{ \large{ - {x}^{2} - 3x + 10 = 0}} \\ \implies{ \large{ {x}^{2} + 3x - 10 = 0}} \\ \implies{ \large{ {x}^{2} + 5x - 2x - 10 = 0}} \\ \implies{ \large{x(x + 5) - 2(x + 5) = 0}} \\ \implies{ \large{(x - 2)(x + 5) = 0}} \\ \implies{ \large{x = 2 \: and \: x = - 5}}$