Identify the LCD of the fractions in the quadratic equation by multiplying the factors of each denominator together. For example, the LCD of the quadratic equation 1 / (x + 1) = 1 - 5 / (2x - 4) is the product of the two denominators: (x + 1)(2x - 4).
Multiply the LCD by both sides of the equation to cancel out all of the denominators. Use the distributive property if there are multiple terms on either side of the equation. In the above example, multiply both sides of the equation by (x + 1)(2x - 4) to get the equation 2x - 4 = (2x - 4)(x + 1) - 5(x + 1).
Expand the resulting quadratic equation using the distributive property and the FOIL method. In the above example, use the FOIL method to expand the product of binomials (x + 1)(2x - 4) to 2x^2 - 4x + 2x - 4. Use the distributive property to expand the product -5(x + 1) to -5x - 5, making the equation 2x - 4 = 2x^2 - 4x + 2x - 4 - 5 - 5x - 5.
Move all terms to one side of the equation, combine like terms and arrange them by descending degree to get the equation in standard form. In the example, subtract the terms 2x and -4 from the left side of the equation and combine the like terms -2x, -4x, 2x and -5x to get -9x and the like terms 4, -4 and -5 to get -5, making the equation 2x^2 - 9x - 5 = 0.
Factor the quadratic equation and use the zero-product principle or use the quadratic formula to solve the quadratic equation. Factor the polynomial 2x^2 - 9x - 5 by grouping: 2x^2 - 10x + x - 5 = 2x(x - 5) + 1(x -5) = (2x + 1)(x - 5). The values of x that make 2x + 1 and x - 5 equal zero are -1/2 and 5, respectively. The solutions to the quadratic equation are x = -1/2 and x = 5.