High School
SAT
ACT
University
MCAT
LSAT
DAT

Solve the following inequality: (2x-1)/(x-5)≥(x+1)/(x+5)

Related Topics

Wize University Calculus 1 Textbook > Pre-Calculus (Review)

Rational Functions

6 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Solve the following inequality: 2x−1x−5≥x+1x+5\dfrac{2x-1}{x-5}\ge\dfrac{x+1}{x+5}
More Rational Functions Questions:
Rational Functions: Slant Asymptote
Find the slant asymptote to the curve y=x3+x2+1x2+1\displaystyle y=\frac{x^3+x^2+1}{x^2+1}.
Rational Functions
Q:\bf{Q:} Find the exact list of vertical asymptotes of f(x)=x−1x2+x\displaystyle f\left(x\right)=\frac{x-1}{x^2+x}
Rational Functions: Slant Asymptote
Find the slant asymptote to the curve y=x3+x2+1x2+1\displaystyle y=\frac{x^3+x^2+1}{x^2+1}.
Q:\bf{Q:} Find f(g(x))f(g(x)) and its domain if f(x)=1x−1f\left(x\right)=\dfrac{1}{x-1} and g(x)=1x+2g\left(x\right)=\dfrac{1}{x+2}
Rational Functions: Inequalities with Fractions
Find all xx that satisfy x+3x2+8x+15≤0\dfrac{x+3}{x^2+8x+15}\le0
Rational Functions
Find all xx that satisfy xx−3≥4\dfrac{x}{x-3}\ge4
Rules of Exponents
Simplify: −5x2ya33z5⋅37xby15z−2-\dfrac{5x^2y^a}{3^3z^5}\cdot\dfrac{3^7x^by}{15z^{-2}}
Rational Functions
Let f(x)=x2+5x+6x−4f(x)=\dfrac{x^2+5x+6}{x-4} be a rational function.
Solving Rational Equations
Practice: Solving Rational Equations
Let f(x)=4x2−252x+5f(x)=\dfrac{4x^2-25}{2x+5}.
If f(x)=4x2−2x+1f(x)=4x^2-2x+1, then what is x?x?
Solving Rational Equations
Practice: Solving Rational Equations
Let f(x)=x2−4x−2f(x)=\dfrac{x^2-4}{x-2}.
If f(x)=x2−5x−6f(x)=x^2-5x-6, then what is x?x?
Solving Rational Equations
Practice: Solving Rational Equations
Given the equation 4xx−5+3x+2=xx2−3x−10\dfrac{4x}{x-5}+\dfrac{3}{x+2}=\dfrac{x}{x^2-3x-10}, answer the following questions.
Solving Rational Equations
Practice: Solving Rational Equations
Given the equation 4x+1−1x+3=x+2x2+4x+3\dfrac{4}{x+1}-\dfrac{1}{x+3}=\dfrac{x+2}{x^2+4x+3}, answer the following questions.
Solving Rational Equations
Practice: Solving Rational Equations
True or false:
8126\dfrac{81}{26} is a solution to 10=4x−13x+810=\dfrac{4x-1}{3x+8}.
Solving Rational Equations
Practice: Solving Rational Equations
True or false:
177\dfrac{17}{7} is a solution to −5=2x+3x−4-5=\dfrac{2x+3}{x-4}.
Solving Rational Equations
Solve for xx:
52x−1−73x+2=96x2+x−2\dfrac{5}{2x-1}-\dfrac{7}{3x+2}=\dfrac{9}{6x^2+x-2}
Solving Rational Equations
Solve 2x−3x2−3=5x+1\dfrac{2x-3}{x^2-3}=\dfrac{5}{x+1}.
Graphing Rational Functions
Practice: Graphing Rational Functions
Write a rational function with the following properties:
An oblique asymptote at y=−3x+1y=-3x+1
Graphing Rational Functions
Practice: Graphing Rational Functions
Write a rational function with the following properties:
An oblique asymptote at y=2x−7y=2x-7
Graphing Rational Functions
Practice: Graphing Rational Functions
Find a rational function of the form f(x)=ax+bcx+df(x)=\displaystyle\frac{ax+b}{cx+d} that describes the following:
Vertical asymptote at x=−1x=-1
Graphing Rational Functions
Practice: Graphing Rational Functions
Find a rational function of the form f(x)=ax+bcx+df(x)=\displaystyle\frac{ax+b}{cx+d} that describes the following:
Vertical asymptote at x=−2x=-2
Graphing Rational Functions
Practice: Graphing Rational Functions
Sketch a graph of f(x)=x2−25x+5f(x)=\dfrac{x^2-25}{x+5}, finding all asymptotes, x-intercepts, missing points, and positive & negative intervals.
Graphing Rational Functions
Practice: Graphing Rational Functions
Sketch a graph of f(x)=−x+9x+3f(x)=\dfrac{-x+9}{x+3}, finding all asymptotes, intercepts, missing points, and positive & negative intervals.
Graphing Rational Functions
Practice: Graphing Rational Functions
A rational function has the following properties:
A horizontal asymptote at y=0y=0.
Graphing Rational Functions
Practice: Graphing Rational Functions
A rational function has the following properties:
A horizontal asymptote at y=0y=0.
Rational Functions
Practice: Rational Functions
Match the equation for the rational function with its appropriate properties.
Rational Functions
Practice: Rational Functions
Match the equation for the rational function with its appropriate properties.
Rational Functions
Practice: Rational Functions
Identify the vertical asymptotes, the horizontal asymptotes, the x-intercepts, and any missing points of:
f(x)=3x2+14x+8x2−2x−14f(x)=\dfrac{3x^2+14x+8}{x^2-2x-14}
Rational Functions
Practice: Rational Functions
Identify the vertical asymptotes, the horizontal asymptotes, the x-intercepts, and any missing points of:
f(x)=2x2+x−12x2+5x−3f(x)=\dfrac{2x^2+x-1}{2x^2+5x-3}
Rational Functions
Practice: Rational Functions
Match the rational function with the correct sketch of its graph.
Rational Functions
Practice: Rational Functions
Match the rational function with the correct sketch of its graph.
Rational Functions
Which of the following graphs is a good approximation of f(x)=x2−3xx+6f(x) = \frac{x^2 - 3x}{x + 6} for xx on the small interval [−1/10,1/10][-1/10, 1/10]
Rational Functions
Match the following five functions with the above graphs.
Rules of Exponents
Simplify: −5x2ya33z5⋅37xby15z−2-\dfrac{5x^2y^a}{3^3z^5}\cdot\dfrac{3^7x^by}{15z^{-2}}
Rational Functions
Q:\bf{Q:} Find the exact list of vertical asymptotes of f(x)=x−1x2+x\displaystyle f\left(x\right)=\frac{x-1}{x^2+x}
Rational Functions: Slant Asymptote
Find the slant asymptote to the curve y=x3+x2+1x2+1\displaystyle y=\frac{x^3+x^2+1}{x^2+1}.
Rational Functions: Inequalities with Fractions
Find all xx that satisfy x+3x2+8x+15≤0\dfrac{x+3}{x^2+8x+15}\le0
Rational Functions
Find all xx that satisfy xx−3≥4\dfrac{x}{x-3}\ge4
Solve the following inequality: 2x−1x−5≥x+1x+5\dfrac{2x-1}{x-5}\ge\dfrac{x+1}{x+5}
Q:\bf{Q:} Find f(g(x))f(g(x)) and its domain if f(x)=1x−1f\left(x\right)=\dfrac{1}{x-1} and g(x)=1x+2g\left(x\right)=\dfrac{1}{x+2}
Rational Functions
Solve the following inequality: 3x+1x−2≤2x−1x+2\frac{3x+1}{x-2}\leq \frac{2x-1}{x+2}
Rational Functions
Solve the following inequality for xx
x−1x+1≤x+2x−1\frac{x-1}{x+1} \leq \frac{x+2}{x-1}
Factoring and Cancelling terms in a Rational Function
When x=2.1x = 2.1 , the function
f(x)=3x2−3x−6x3−2x2−x+2f(x) = \frac{3x^2 - 3x - 6}{x^3 - 2x^2 - x + 2}
is closest to which number?
Evaluating Rational Functions at a Point
When x=−100x = -100 , the function
f(x)=−3x16−2x10−x3+215x13+2x10−x5+3f(x) = \frac{-3 x^{16} - 2 x^{10} - x^3 + 2}{15 x^{13} + 2 x^{10} - x^5 + 3}
is closest to which number?
Rational Functions
When x=0.01x = 0.01 the function
f(x)=3x9+7x3−105x8−3x7+2xf(x) = \frac{3x^9 + 7x^3 - 10}{5x^8 -3x^7 + 2x}
is closest to which number?
Rational Functions
When x=1000x = 1000 the function
f(x)=3x9+7x3−105x8−3x7+2xf(x) = \frac{3x^9 + 7x^3 - 10}{5x^8 -3x^7 + 2x}
is closest to which number?