Question

Find the domain of the function : Can you show the steps

Answer 1

A rational function must not have a denominator of 0, since that means the divisor is a 0 and there's no number whatsoever you can multiply it with 0 to get the dividend, the short version of all that is, the fraction is "undefined".

a domain for a rational is any values of "x" that are safe, namely will not make the denominator undefined, there are a few other constraints, but this is the only one in this case.

so, what values "x" cannot take on safely?  well, we can find out what makes the denominator to 0, by simply, yeap, you guessed it, zeroing it out, let's do so,

 $\bf 5x+2=0\implies 5x=-2\implies x=-\cfrac{2}{5}$

so, if ever "x" becomes -2/5, our handy dandy fraction will go poof.

so the domain is all real numbers for "x", EXCEPT -2/5, or in Set Builder notation, {x | x ∈ ℝ; x ≠ -⅖}