Answer
$\displaystyle \frac{3}{y-3}$
Work Step by Step
To subtract rational expressions with the same denominator,
subtract numerators and place the difference over the common denominator.
If possible, factor and simplify the result.
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Don't forget to place the second numerator in parentheses when subtracting.
$\displaystyle \frac{y^{2}+3y}{y^{2}+y-12}-\frac{y^{2}-12}{y^{2}+y-12}= \displaystyle \frac{y^{2}+3y-(y^{2}-12)}{y^{2}+y-12}$
$= \displaystyle \frac{y^{2}+3y-y^{2}+12}{y^{2}+y-12}$
$= \displaystyle \frac{3y+12}{y^{2}+y-12}\qquad$... factor what we can...
... Numerator: the gcf is 3
... Denominator: two factors of -12 whose sum is 1... are -3 and +4.
$=\displaystyle \frac{3(y+4)}{(y-3)(y+4)}$
... reduce (divide the numerator and denominator with common factors)
$=\displaystyle \frac{3}{y-3}$
