solve the equation. check the solution. use a graphing calculator.

\\frac{3}{x+5} + \frac{4}{x-5} = 2\

select the correct choice and fill in any answer boxes in your choice below.

a. the solution is $x = -3.78, 7.28$.
(round to two decimal places as needed. use a comma to separate answers as needed.)

b. there is no solution.

Question

solve the equation. check the solution. use a graphing calculator.

\\frac{3}{x+5} + \frac{4}{x-5} = 2\

select the correct choice and fill in any answer boxes in your choice below.

a. the solution is $x = -3.78, 7.28$.
(round to two decimal places as needed. use a comma to separate answers as needed.)

b. there is no solution.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Rational Equations", "Quadratic Formula" ], "new_concepts": [], "current_concepts": [ "Rational Equations", "Quadratic Formula", "Extraneous Solutions" ] } ## Clear denominators $$ \begin{aligned} &\frac{3}{x+5} + \frac{4}{x-5} = 2,\quad x e \pm 5\ &3(x-5) + 4(x+5) = 2(x+5)(x-5)\ &3x - 15 + 4x + 20 = 2(x^2 - 25)\ &7x + 5 = 2x^2 - 50 \end{aligned} $$ ## Rearrange to standard quadratic form $$ \begin{aligned} &2x^2 - 7x - 55 = 0 \end{aligned} $$ ## Solve using the quadratic formula $$ \begin{aligned} &x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(2)(-55)}}{2(2)}\ &x = \frac{7 \pm \sqrt{49 + 440}}{4}\ &x = \frac{7 \pm \sqrt{489}}{4}\ &x_1 = \frac{7 + 22.1133}{4} \approx 7.28\ &x_2 = \frac{7 - 22.1133}{4} \approx -3.78 \end{aligned} $$

(A) The solution is $x = -3.78, 7.28$

(B) There is no solution.

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Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Clear denominators

Rearrange to standard quadratic form

Solve using the quadratic formula

Answer: