Question 92801
Given:
.
{{{y=(3x-2)/(4x+1)}}}
.
The domain is the spectrum of values that x can take. In this problem there is only one
consideration that limits the value of x. Notice that there is a denominator that contains x.
Also recall that algebraic rules do not permit division by zero. Therefore, the denominator
cannot equal zero.
.
So we can write the equation:
.
{{{4x + 1 = 0}}}
.
Subtract 1 from both sides and we get:
.
{{{4x = -1}}}
.
Finally, divide both sides by 4 to find x and you get:
.
{{{x = (-1)/4}}}
.
This tells us that if {{{x = (-1)/4}}} then the denominator equals zero. Therefore,
x cannot be equal to {{{(-1)/4}}}. Other than that single exception, x can have any value 
from minus infinity to plus infinity.
.
Hope this helps you to understand the problem a little more.