What is the range of the function h(x) = frac | vedclass

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(B) To find the range of the function $h(x) = \frac{x-2}{x+3}$,let $h(x) = y$.Set $y = \frac{x-2}{x+3}$.Multiply both sides by $(x+3)$:$y(x+3) = x-2$$

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$(-\infty, 1) \cup (1, \infty)$

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(B) To find the range of the function $h(x) = \frac{x-2}{x+3}$,let $h(x) = y$.Set $y = \frac{x-2}{x+3}$.Multiply both sides by $(x+3)$:$y(x+3) = x-2$$xy + 3y = x - 2$Rearrange to solve for $x$:$xy - x = -3y - 2$$x(y-1) = -(3y + 2)$$x = \frac{-(3y+2)}{y-1} = \frac{3y+2}{1-y}$.For $x$ to be defined,the denominator $1-y 
eq 0$,which means $y 
eq 1$.Thus,the range of the function is all real numbers except $1$,which is $(-\infty, 1) \cup (1, \infty)$.

What is the range of the function $h(x) = \frac{x-2}{x+3}$?

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