Question

Select the correct answer.
Which quadratic equation is part of the solution process for solving this rational equation using the least common denominator?
.6
35 + 6
OA 12 + 1 - 2 = 0
OB. 12 + 1 + 10 = 0
OC. 2 - - 2 = 0
OD.
12 – 1 – 10 = 0

Answer 1

Answer:

D)  x² -x - 10  =0

Step-by-step explanation:

Given that

             $\frac{2}{3x-6} - \frac{1}{3x+6} = \frac{1}{3}$

L.C.M

         $\frac{2(3x+6)-(3x-6)}{(3x+6)(3x-6)} = \frac{1}{3}$

        $\frac{(6x+12-3x+6)}{(3x+6)(3x-6)} = \frac{1}{3}$

          $\frac{(3x+18)}{((3x)^{2} )-(6)^{2} } = \frac{1}{3}$

    ⇒ $3(3x+18) = 9 x^{2} - 36$

   ⇒ 9 x + 54 = 9 x² - 36

  ⇒ 9 x² - 36 - 9x - 54 =0

⇒ 9 x²  - 9x - 90 =0

⇒ 9(x² -x - 10 ) =0

⇒ x² -x - 10  =0