find the equation of the slant asymptote of the function $f(x) = \frac{x^2 + x + 4}{x - 1}$.

a) $y = x + \frac{6}{x - 1}$
b) $y = x + 2$
c) $y = x - 2$
d) $y = x$

question 5 (5 points)
solve for $x$.
$\frac{x}{2} = \frac{3x + 4}{2x}$

a) $x = 4, 1/2$
b) $x = -4, 1$
c) $x = 4, -1/2$
d) $x = 4, -1$

question 6 (5 points)
solve the equation: $\frac{1}{x - 8} - 1 = -\frac{7}{x - 8}$

a) $x = 2$
b) $x = 4$
c) $x = 16$
d) $x = 0$

Question

find the equation of the slant asymptote of the function $f(x) = \frac{x^2 + x + 4}{x - 1}$.

a) $y = x + \frac{6}{x - 1}$
b) $y = x + 2$
c) $y = x - 2$
d) $y = x$

question 5 (5 points)
solve for $x$.
$\frac{x}{2} = \frac{3x + 4}{2x}$

a) $x = 4, 1/2$
b) $x = -4, 1$
c) $x = 4, -1/2$
d) $x = 4, -1$

question 6 (5 points)
solve the equation: $\frac{1}{x - 8} - 1 = -\frac{7}{x - 8}$

a) $x = 2$
b) $x = 4$
c) $x = 16$
d) $x = 0$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slant Asymptotes", "Rational Equations" ], "new_concepts": [], "current_concepts": [ "Slant Asymptotes", "Rational Equations", "Polynomial Long Division" ] } ## Find the slant asymptote of $f(x) = \frac{x^2+x+4}{x-1}$ $$ \begin{aligned} f(x) &= \frac{x(x-1) + 2x + 4}{x-1} = x + \frac{2(x-1) + 6}{x-1} = x + 2 + \frac{6}{x-1} \ \lim_{x \to \pm\infty} [f(x) - (x+2)] &= \lim_{x \to \pm\infty} \frac{6}{x-1} = 0 \implies y = x + 2 \end{aligned} $$ ## Solve the equation $\frac{x}{2} = \frac{3x+4}{2x}$ $$ \begin{aligned} x(2x) &= 2(3x+4) \quad (x eq 0) \ 2x^2 &= 6x + 8 \ x^2 - 3x - 4 &= 0 \ (x-4)(x+1) &= 0 \implies x = 4, -1 \end{aligned} $$ ## Solve the equation $\frac{1}{x-8} - 1 = -\frac{7}{x-8}$ $$ \begin{aligned} \frac{1}{x-8} + \frac{7}{x-8} &= 1 \quad (x eq 8) \ \frac{8}{x-8} &= 1 \ x-8 &= 8 \implies x = 16 \end{aligned} $$ ## Question 1 (A) $y = x + 6/(x-1)$

(B) $y = x + 2$

(C) $y = x - 2$

(D) $y = x$ ## Question 2 (A) $x = 4, 1/2$

(B) $x = -4, 1$

(C) $x = 4, -1/2$

(D) $x = 4, -1$ ## Question 3 (A) $x = 2$

(B) $x = 4$

(C) $x = 16$

(D) $x = 0$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Rational Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Find the slant asymptote of \(f(x) = \frac{x^2+x+4}{x-1}\)

Solve the equation \(\frac{x}{2} = \frac{3x+4}{2x}\)

Solve the equation \(\frac{1}{x-8} - 1 = -\frac{7}{x-8}\)

Answer:

Question 1

Question 2

Question 3