Solve the forlowing rational & fuation [ (5)/(x^2)-4-(8)/(x^2)-1=(2)/(x^2)-3 x+2-(20)/(x^2)-3 x+2 ]

To solve the given rational equation, we first need to simplify and find a common denominator for each side of the equation.The equation is: First, let's factor each quadratic expression in the denominators:1. can be factored as \((x-2)(x+2)\).2. can be factored as \((x-1)(x+1)\).3. can be factored as \((x-1)(x-2)\).Now, rewrite the equation with these factored forms: Simplify the right-hand side: Now the equation becomes: To solve this equation, we need a common denominator for all terms. The least common denominator (LCD) is \((x-2)(x+2)(x-1)(x+1)\).Rewrite each term with the LCD:- The first term: \(\frac{5}{(x-2)(x+2)}\) becomes \(\frac{5(x-1)(x+1)}{(x-2)(x+2)(x-1)(x+1)}\).- The second term: \(\frac{8}{(x-1)(x+1)}\) becomes \(\frac{8(x-2)(x+2)}{(x-2)(x+2)(x-1)(x+1)}\).- The third term: \(\frac{-18}{(x-1)(x-2)}\) becomes \(\frac{-18(x+2)}{(x-2)(x+2)(x-1)(x+1)}\).Now, combine the fractions: Since the denominators are the same, equate the numerators: Expand and simplify each term:- \(5(x-1)(x+1) = 5(x^2 - 1) = 5x^2 - 5\)- \(8(x-2)(x+2) = 8(x^2 - 4) = 8x^2 - 32\)- \(-18(x+2) = -18x - 36\)Substitute back into the equation: Simplify: Rearrange all terms to one side: Divide the entire equation by to simplify: Solve this quadratic equation using the quadratic formula: where , , and .Calculate the discriminant: Thus, the solutions are: Simplify : So the solutions are: Therefore, the solutions to the equation are and .