Solve!!!!!!!!!!!!!!!!!!!!

Question

x^2 -4x / x^2-1 < 0?

Answer 1

The inequality is

• Step-1

State the exclude values,these are the values for which denominator is zero.

The exclude value of the inequality is 1,-1.

• Step - 2

Solve the related equation

Solutions of related equation x   = 0 and x  = 4.

• Step-3

Draw the vertical lines at the exclude values and at the solutions to separate the number line into intervals.

• Step-4

Now test  sample values in each interval to determine whether values in the interval satisfy the inequality.

Test interval   x - value      Inequality                                   Conclusion

(-∞, -1)                x =  -2                          False

(-1, 0)                  x = -0.5              True

(0, 1)                  x = 0.5                   False

(1, 4)                  x = 2                         True

(4, ∞)                x = 5                           False

The above conclude that the inequality is satisfied for all x - values in (-1, 0) U (1, 4) as shown in Figure below.

Solution - 1 < x  < 0

1 < x  < 4