\frac{1}{x {}^(2) - 3 } = ( √(3) )/(x + √(3) ) - (2)/( √(3) - x ) can someone please solve this? ​

Question

`\frac{1}{x {}^(2) - 3 } = ( √(3) )/(x + √(3) ) - (2)/( √(3) - x )`

can someone please solve this?
​

Answer 1

`\boxed{\textsf{ The value of x is \textbf{ 8 + 6}$√(3 )$.}}`

Explanation:

Here we are given a equation which we need today simplify and solve for x .The given equation to us is :-

`\sf\implies \frac{1}{x {}^(2) - 3 } = ( √(3) )/(x + √(3) ) - (2)/( √(3) - x )`

Let's simplify the equation :-

`\sf\implies \frac{1}{x {}^(2) - 3 } = ( √(3) )/(x + √(3) ) - (2)/( √(3) - x ) \\\\\sf\implies (1)/(x^2-3)=(\sqrt3)/(x+\sqrt3)-(2)/(-(x-\sqrt3))\\\\\sf\implies (1)/(x^2-3)=(\sqrt3)/(x+\sqrt3)+(2)/(x-\sqrt3)\\\\\sf\implies (1)/(x^2-3)=(\sqrt3(x-\sqrt3)+2(x+\sqrt3))/((x+\sqrt3)(x-\sqrt3))\\\\\sf\implies (1)/(x^2-3)=(\sqrt3x-3+2x+2\sqrt3)/(x^2-3)\\\\\sf\implies 1=\sqrt3x-3+2x+2\sqrt3 \\\\\sf\implies \sqrt3x+2x = 4-2\sqrt3\\\\\sf\implies x(\sqrt3 +2)=4-2\sqrt3\\\\\sf\implies x =(4-2\sqrt3)/(\sqrt3+2)\\\\\sf\implies x =( (4-2\sqrt3)(\sqrt3-2))/((\sqrt3+2)(\sqrt3-2))\\\\\sf\implies x =(-8-6√(3))/(3-4)\\\\\sf\implies \boxed{\pink{\sf x =8+6\sqrt3}}`