How do you find the domain and range of y=(-4x-3)/(x-2)

How do you find the domain and range of $y=\frac{-4x-3}{x-2}$?
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The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.
solve $x-2=0⇒x=2←$ excluded value
domain is $x\in \mathbb{R},x\ne 2$
Rearrange the function and make x the subject
$⇒y\left(x-2\right)=-4x-3$
$⇒xy-2y=-4x-3$
$⇒xy+4x=2y-3$
$⇒x\left(y+4\right)=2y-3$
$⇒x=\frac{2y-3}{y+4}$
Again the denominator cannot be zero.
solve $y+4=0⇒y=-4←$ excluded value
range is $y\in \mathbb{R},y\ne -4$