Question

solve: x-1 / x+2 >1, x+3 / x-1 >2.
please help, my answer is not coming right.

Answer 1

Solve: $x - 1 / x + 2 > 1, x + 3 / x - 1 > 2$ .

Solution:

The first inequality

$$\frac {x - 1}{x + 2} > 1$$

Portable 1 to the left and lead to a common denominator:

$$\begin{array}{l} \frac {x - 1}{x + 2} - 1 > 0 \\ \frac {x - 1 - x - 2}{x + 2} > 0 \\ - \frac {3}{x + 2} > 0 \\ x \in (- \infty ; - 2) \\ \end{array}$$

The second inequality:

$$\frac {x + 3}{x - 1} > 2$$

Portable 2 to the left and lead to a common denominator:

$$\begin{array}{l} \frac {x + 3}{x - 1} - 2 > 0 \\ \frac {x + 3 - 2 x + 2}{x - 1} > 0 \\ - \frac {x - 5}{x - 1} > 0 \\ x \in (1; 5) \\ \end{array}$$

Answer: 1. $x \in (-\infty; -2)$

2. $x \in (1; 5)$