Question:

Find every value of the variable that makes each rational expression undefined.

1. [tex] \displaystyle \frac{3x}{4x + 15} [/tex]

2. [tex] \displaystyle \frac{5x}{5x - 5} [/tex]

What to do:

To make rational expression undefined is to make the denominator equal to 0. This can be done by equating the denominator to 0.

Solution/s:

1.

The denominator is [tex] 4x + 15 [/tex].

Equate to 0:

[tex] 4x + 15 = 0 [/tex]

Solve for [tex]x[/tex]:

[tex] 4x = -15 [/tex]

[tex] \displaystyle \boxed{x = -\frac{15}{4}} [/tex]

2.

The denominator is [tex] 5x - 5 [/tex].

Equate to 0:

[tex] 5x - 5 = 0 [/tex]

Solve for [tex]x[/tex]:

[tex] 5x = 5 [/tex]

[tex] \boxed{x = 1} [/tex]

Answer:

1. [tex]\displaystyle \boxed{x = -\frac{15}{4}} [/tex]

2. [tex] \boxed{x = 1} [/tex]