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

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

Answer 2

`\boldsymbol{\sf{(x)/(x-2)+(1)/(x-6)=(4)/(x^(2) -8x+12 ) }}`

We factor the expression.

`\boldsymbol{\sf{(x)/(x-2)+(1)/(x-6)=(4)/((x-6)(x-2) ) }}`

Multiply both sides of the equation by the common denominator.

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

Simplify fractions

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

`\boldsymbol{\sf{x(x-6)+x-2=(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