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第四章:部分分式 Partial Fraction

第六章:角的形成及单位 Angles and Measurements

第十三章: 方程组 Simultaneous Equations

第十五章:二元一次不等式及线性规划 linear inequality in two variables and linear programming

14.6 分式不等式 Rational Inequalities
14.6 Rational Inequalities 分式不等式


Solve the inequalities
解下列不等式

(1)
(a) \frac{(x-3)(x+1)}{(x-1)(x+3)} < 0

(b) \frac{(x-3)(x+1)}{(x-1)(x+3)}\le0

Answer:

(a) –3 < x < –1, 1 < x < 3

(b) –3 < x \leq –1, 1 < x \leq 3

(2)

\frac{2+3x-x^2}{x-1}\le0

Answer:
\frac{1}{2}(3 - \sqrt{17}) \leq x < 1,

x \geq \frac{1}{2}(3 + \sqrt{17})

(3)

\frac{x-2}{2-2x} < -\frac{2}{3}

Answer:
-2 < x < 1
(4)

\frac{10}{x}\le19-6x

Answer:
x < 0, \frac{2}{3} \leq x \leq 2\frac{1}{2}
(5)

\frac{1}{x-1}<\frac{1}{x+1}

Answer:
-1 < x < 1
(6)

\frac{x-4}{x-2}\geq\frac{x-3}{x+1}

Answer:
-1 < x < 2, x \geq 5
(7)

\frac{(x^2+x-6)(2x^2-5x+2)}{x^2+2x+3}\le0

Answer:
-3 \leq x \leq \frac{1}{2}, x = 2
(8)

\frac{x+1}{x-1}-\frac{3}{x^2-1}\le1

Answer:
x < -1, \frac{1}{2}\leq x < 1