ex Solve the inequality.
\displaystyle
\frac{1}{x + 1} - \frac{1}{2x + 3} \leq 0
Solutions
x \in (-\infty, -2) \cup (-\frac{3}{2}, -1)
ex Solve for x.
\displaystyle
\frac{x^2 -4}{(x -1)(x^3 -27)} \leq 0
ex Solve for x.
\displaystyle
\frac{(-x^2-3)(x^2-5x + 4)}{x^2 + 1} \geq 0
Solutions
x \in [1, 4]
ex Solve for x.
\displaystyle
\frac{1}{x} + \frac{1}{x -1} -\frac{1}{x + 5} \geq 0
Solutions*
x \in [-5\sqrt{30}, -5]\cup (0, -5|\sqrt{30}]
Determine the x-intercept(s) for each function.
\displaystyle
y = \frac{x + 1}{x}
Determine the x-intercept(s) for each function.
\displaystyle
f(x) = \frac{x^2 + x - 12}{x^2 -3x + 5}
Determine the x-intercept(s) for each function.
\displaystyle
h(x) = \frac{2x-3}{5x + 1}
Determine the x-intercept(s) for each function.
\displaystyle
k(x) = \frac{x}{x^2 -3x+ 2}
Solve algebraically.
\displaystyle
\frac{4}{x - 2} = 3
Solve algebraically.
\displaystyle
\frac{1}{x^2 -2x - 7} =1
Solve algebraically.
\displaystyle
\frac{2}{x-1} = \frac{5}{x + 3}
Solve algebraically.
\displaystyle
x - \frac{5}{x} = 4
Solve algebraically.
\displaystyle
\frac{1}{x} = \frac{x - 34}{2x^2}
Solve algebraically.
\displaystyle
\frac{x -3}{x -4} = \frac{x + 2}{x + 6}
Solve the inequality.
\displaystyle
\frac{4}{x - 3} < 1
Solve the inequality.
\displaystyle
\frac{7}{x+ 1} > 7
Solve the inequality.
\displaystyle
\frac{5}{x+ 4} \leq \frac{2}{x + 1}
Solve the inequality.
\displaystyle
\frac{(x-2)(x+1)^2}{(x - 4)(x+5)} \geq 0
Solve the inequality.
\displaystyle
\frac{x^2-16}{x^2 -4x - 5} > 0
Solve the inequality.
\displaystyle
\frac{x-2}{x} > \frac{x -4}{x - 6}
Solve each this inequality.
\displaystyle
\frac{x^2 + 9x + 14}{x^2 -6x + 5} > 0
Solve each this inequality.
\displaystyle
\frac{2x^2 + 5x -3}{x^2 + 8x + 16} < 0
Solve each this inequality.
\displaystyle
\frac{x^2 - 3x - 4}{x^2 + 11x + 30} \leq 0
Solve each this inequality.
\displaystyle
\frac{3x^2 - 8x + 4}{2x^2 - 9x - 5} \geq 0
Write a rational equation that cannot have x = 3 or x = -5 as a solution.
Solve \frac{x}{x + 1} < \frac{2x}{x - 2} by graphing the functions f(x) = \frac{x}{x + 1} and g(x) = \frac{2x}{x -2} with or without using technology. Determine the points of intersection and when f(x) < g(x).
Solve \displaystyle \frac{x}{x -3} > \frac{3x}{x + 5} by graphing two rational functions on a graphing device..
Solve.
\displaystyle
\frac{1}{x} + 3 = \frac{2}{x}
Solve.
\displaystyle
\frac{2}{x + 1} + 5 = \frac{1}{x}
Solve.
\displaystyle
\frac{12}{x} + x = 8
Solve.
\displaystyle
\frac{x}{x - 1} = 1 - \frac{1}{1 -x}
Solve.
\displaystyle
\frac{2x}{2x +3} -\frac{2x}{2x - 3} = 1
Solve.
\displaystyle
\frac{7}{x - 2} - \frac{4}{x - 1}+ \frac{3}{x + 1} = 0
Solve the inequality.
\displaystyle
\frac{2}{x} + 3 > \frac{29}{x}
Solve the inequality.
\displaystyle
\frac{16}{x } -5 < \frac{1}{x}
Solve the inequality.
\displaystyle
\frac{5}{6x} + \frac{2}{3x} > \frac{3}{4}
Solve the inequality.
\displaystyle
6 + \frac{30}{x - 1} < 7
The ratio of x + 2 to x - 5 is greater than \frac{3}{5}. Solve for x.
Compare the solutions to \displaystyle \frac{2x -1}{x + 7} > \frac{x + 1}{x + 3}
and \displaystyle \frac{2x - 1}{x+ 7} < \frac{x +1}{x + 3}
Compare the solutions to
i. \displaystyle \frac{x + 1}{x-4} > \frac{x -3}{x + 5}
ii. and \displaystyle \frac{x -4}{x + 7} < \frac{x +5}{x - 3}
A number x is the harmonic mean of two numbers a and b is the mean of \frac{1}{a} and \frac{1}{b}.
a and b.A number x is the harmonic mean of two numbers a and b is the mean of \frac{1}{a} and \frac{1}{b}.
A number x is the harmonic mean of two numbers a and b is the mean of \dfrac{1}{a} and \dfrac{1}{b}.
The relationship between the object distance, d, and image distance, I, both in centimetres, for a camera with focal length 2.0cm is defined by the relation d = \dfrac{2.0I}{I - 2.0}. For what values of I is a d greater than 10.0 cm?
Consider the functions f(x) = \frac{1}{x} + 4 and g(x) = \frac{2}{x}. Graph f and g on the same grid.
Consider the functions f(x) = \frac{1}{x} + 4 and g(x) = \frac{2}{x}. Graph f and g on the same grid.
f(x) < g(x).\frac{1}{x} + 4 = \frac{2}{x}.A rectangle has perimeter 64 cm and area 23 crn^2. Solve the following system of equations to find the rectangle’s width.
\displaystyle
l = \frac{23}{w}
\displaystyle
l + 2 = 32
Solve the system of equations.
\displaystyle
\begin{array}{cccccc}
&x^2 + y^2 = 1 \\
&xy = 0.5 \\
\end{array}
Use your knowledge of exponents to solve.
\displaystyle
\frac{1}{2^x} = \frac{1}{x + 2}
Use your knowledge of exponents to solve.
\displaystyle
\frac{1}{2^x} = \frac{1}{x^2}
Determine the region(s) of the Cartesian plane for which
\displaystyle
y > \frac{1}{x^2}
Determine the region(s) of the Cartesian plane for which
\displaystyle
y\leq x^2 +4
and
\displaystyle
y \geq \frac{1}{x^2 + 4}
Decompose each of the following into partial fractions.
\displaystyle
f(x) = \frac{5x + 7}{x^2 + 2x - 3}
Decompose each of the following into partial fractions.
\displaystyle
f(x) = \frac{7x +6}{x^2-x-6}
Decompose each of the following into partial fractions.
\displaystyle
h(x) = \frac{6x^&2-14x-27}{(x + 2)(x -3)^2}