Find the least common denominator for the following rational expressions. (r – 1)(r – 4)(r – 5) (r – 1)(r + 4)(r – 5) (r – 1)(r + 1)(r – 4)(r – 5) (r – 1)(r + 1)(r + 4)(r – 5)

(r - 4)(r - 1)(r - 5)(r + 1)

Step-by-step explanation:

We can simply look at the denominators and factor them.

First: (r - 4).

Second: (r - 4) (r - 1).

Third: (r - 5)(r + 1).

In order to find the LCD, simply create a common denominator.

The smallest value that would make this rational expression have a common denominator would be:

(r - 4)(r - 1)(r - 5)(r + 1).

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is