4/((x-1))>= 1/((2x-1))

解答

\frac{4}{( x - 1 )} \geq \frac{1}{( 2 x - 1 )}

\frac{3}{7} \leq x < \frac{1}{2} or x > 1

间隔符号

[\frac{3}{7}, \frac{1}{2}) \cup (1, \infty)

十进制

0.42857 \dots \leq x < 0.5 or x > 1

求解步骤

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

改写为标准形式

\frac{7 x - 3}{( x - 1 ) ( 2 x - 1 )} \geq 0

确定区间

\frac{3}{7} \leq x < \frac{1}{2} or x > 1

\frac{( x - 5 )}{( x ^{2} + x + 5 ) ( x ^{2} - 4 x - 5 )} > 0

\frac{( ( x - 1 ) ^{2} \cdot ( x + 1 ) ^{3} )}{( x ^{4} \cdot ( x - 2 ) )} \leq 0

(x^{2} - 1) (x - 2) > 0

(x^{2} - x)^{2} + 3 (x^{2} - x) > 0

\frac{3}{( 2 x - 1 )} \geq \frac{5}{( x - 1 )}