Question

I am in need of assistance.

Answer 1

Answer:

A. x = 6.08, x = -0.58

Step-by-step explanation:

• $\displaystyle \frac{2x}{x-4}-\frac{2x-5}{x^2-10x+24}=\frac{-3}{x-6}$

1. Factor the denominator.

• $\displaystyle \frac{2x}{x-4}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

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

• $\displaystyle \Big ( \frac{x-6}{x-6} \Big ) \frac{2x}{x-4}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$

3. Simplify.

• $\displaystyle \frac{2x^2-12x}{(x-4)(x-6)}-\frac{2x-5}{(x-6)(x-4)}=\frac{-3}{x-6}$  

4. Combine like terms.

• $\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3}{x-6}$  

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

• $\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3}{x-6} \Big ( \frac{x-4}{x-4} \Big )$  

6. Simplify.

• $\displaystyle \frac{2x^2-14x+5}{(x-4)(x-6)}=\frac{-3x+12}{(x-6)(x-4)}$

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

• $2x^2-14x+5=-3x+12$

8. Set the equation equal to 0.

• $2x^2-11x-7=0$

Quadratic formula:

• $\displaystyle x = \frac{-b\pm \sqrt{b^2-4ac} }{2a}$  

9. Factor using the quadratic formula.

• $\displaystyle x = \frac{-(-11)\pm \sqrt{(-11)^2-4(2)(-7)} }{2(2)}$

10. Multiply and simplify.

• $\displaystyle x = \frac{11 \pm \sqrt{177} }{4}$

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.