Question

Solve the equation.

x/x−2 + 1/x−6 =4/x^2−8x+12

Drag the choice or choices into the box to correctly state the solution to the equation.

Answer 1

$\boldsymbol{\sf{\dfrac{x}{x-2}+\dfrac{1}{x-6}=\dfrac{4}{x^{2} -8x+12 } }}$

We factor the expression.

         $\boldsymbol{\sf{\dfrac{x}{x-2}+\dfrac{1}{x-6}=\dfrac{4}{(x-6)(x-2) } }}$

Multiply both sides of the equation by the common denominator.

            $\boldsymbol{\sf{\dfrac{x(x-2)(x-6)}{x-2}+\dfrac{(x-2)(x-6)}{x-6}=\dfrac{4(x-2)(x-6)}{(x-6)(x-2)} }}$

Simplify fractions

              $\boldsymbol{\sf{x(x-6)+\dfrac{(x-2)(x-6)}{x-6}=\dfrac{4(x-2)(x-6)}{(x-6)(x-2)} }}$

                $\boldsymbol{\sf{x(x-6)+x-2=\dfrac{4(x-2)(x-6)}{(x-6)(x-2)} }}$

                    $\boldsymbol{\sf{x(x-6)+x-2=4 }}$

Apply the multiplicative law of distribution.

                  $\boldsymbol{\sf{x^{2} -6x+x-2=4 }}$

Combine as terms.

                      $\boldsymbol{\sf{x^{2} -5x-2=4 }}$

Move all terms to the side of the equation.

                        $\boldsymbol{\sf{x^{2} -5x-2-4=0 }}$

Combine as terms

                        $\boldsymbol{\sf{x^{2} -5x-6=0 }}$

Separate the middle term into two terms.

                           $\boldsymbol{\sf{x^{2} -6x+x-6=0 }}$

Factor the first two terms and the last two terms respectively.

                      $\boldsymbol{\sf{x(x-6)+(x-6)=0 }}$

Take out the common factor

                       $\boldsymbol{\sf{(x-6)(x+1)=0}}$

If the product of the two factors is equal to 0, then at least one factor is 0.

                        $\boldsymbol{\sf{x-6=0 \ or \ x+1=0 }}$

Order the unknown terms on the left side of the equation.

                                $\boldsymbol{\sf{x=6 \ or \ x=-1}}$

Find the intersection

                          $\green{\boxed{\boldsymbol{\sf{\green{Answer \ \ \longmapsto \ x=-1}}}}}$

Skandar

Answer 2

I hope it's helpful .......