Answer
$4-y$
Work Step by Step
Simplifying Rational Expressions
1. Factor the numerator and the denominator completely.
2. Divide both the numerator and the denominator by any common factors.
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Numerator $:$ search for two factors of $12$ whose sum is $-7$
... these are $-4$ and $-3$
$y^{2}-7y+12=(y-4)(y-3)$
Denominator = $-(y-3)$
Expression = $\displaystyle \frac{(y-4)(y-3)}{-(y-3)}$
... divide both with the common factor: $(y-3)$
Expression = $\displaystyle \frac{y-4}{-1}$ = $-(y-4)$ = $-y+4$
= $4-y$
