Question

I am in need of assistance.

Answer 1

A. x = 6.08, x = -0.58

Explanation:

• 
  `\displaystyle (2x)/(x-4)-(2x-5)/(x^2-10x+24)=(-3)/(x-6)`

1. Factor the denominator.

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  `\displaystyle (2x)/(x-4)-(2x-5)/((x-6)(x-4))=(-3)/(x-6)`

2. Multiply the leftmost fraction by (x-6)/(x-6) to get common denominators.

• 
  `\displaystyle \Big ( (x-6)/(x-6) \Big ) (2x)/(x-4)-(2x-5)/((x-6)(x-4))=(-3)/(x-6)`

3. Simplify.

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  `\displaystyle (2x^2-12x)/((x-4)(x-6))-(2x-5)/((x-6)(x-4))=(-3)/(x-6)`

4. Combine like terms.

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  `\displaystyle (2x^2-14x+5)/((x-4)(x-6))=(-3)/(x-6)`

5. Multiply the right side of the equation by (x-4)/(x-4).

• 
  `\displaystyle (2x^2-14x+5)/((x-4)(x-6))=(-3)/(x-6) \Big ( (x-4)/(x-4) \Big )`

6. Simplify.

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  `\displaystyle (2x^2-14x+5)/((x-4)(x-6))=(-3x+12)/((x-6)(x-4))`

7. "Cancel" out the denominators because they are equivalent.

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  `2x^2-14x+5=-3x+12`

8. Set the equation equal to 0.

• 
  `2x^2-11x-7=0`

Quadratic formula:

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  `\displaystyle x = (-b\pm √(b^2-4ac) )/(2a)`

9. Factor using the quadratic formula.

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  `\displaystyle x = (-(-11)\pm √((-11)^2-4(2)(-7)) )/(2(2))`

10. Multiply and simplify.

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  `\displaystyle x = (11 \pm √(177) )/(4)`

11. Plug this into your calculator and solve for x.

• 
  `x=6.07603367 \approx 6.08`
• 
  `x=-0.57603367 \approx -0.58`

The correct answer is A. x = 6.08, x = -0.58.