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$\fraction{4 y + 9}{\exponential{y}{2} + 2 y - 24} + \fraction{7}{\exponential{y}{2} + 5 y - 6} $
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\frac{4y+9}{\left(y-4\right)\left(y+6\right)}+\frac{7}{\left(y-1\right)\left(y+6\right)}
Factor y^{2}+2y-24. Factor y^{2}+5y-6.
\frac{\left(4y+9\right)\left(y-1\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}+\frac{7\left(y-4\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(y-4\right)\left(y+6\right) and \left(y-1\right)\left(y+6\right) is \left(y-4\right)\left(y-1\right)\left(y+6\right). Multiply \frac{4y+9}{\left(y-4\right)\left(y+6\right)} times \frac{y-1}{y-1}. Multiply \frac{7}{\left(y-1\right)\left(y+6\right)} times \frac{y-4}{y-4}.
\frac{\left(4y+9\right)\left(y-1\right)+7\left(y-4\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
Since \frac{\left(4y+9\right)\left(y-1\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)} and \frac{7\left(y-4\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)} have the same denominator, add them by adding their numerators.
\frac{4y^{2}-4y+9y-9+7y-28}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
Do the multiplications in \left(4y+9\right)\left(y-1\right)+7\left(y-4\right).
\frac{4y^{2}+12y-37}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
Combine like terms in 4y^{2}-4y+9y-9+7y-28.
\frac{4y^{2}+12y-37}{y^{3}+y^{2}-26y+24}
Expand \left(y-4\right)\left(y-1\right)\left(y+6\right).
\frac{4y+9}{\left(y-4\right)\left(y+6\right)}+\frac{7}{\left(y-1\right)\left(y+6\right)}
Factor y^{2}+2y-24. Factor y^{2}+5y-6.
\frac{\left(4y+9\right)\left(y-1\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}+\frac{7\left(y-4\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(y-4\right)\left(y+6\right) and \left(y-1\right)\left(y+6\right) is \left(y-4\right)\left(y-1\right)\left(y+6\right). Multiply \frac{4y+9}{\left(y-4\right)\left(y+6\right)} times \frac{y-1}{y-1}. Multiply \frac{7}{\left(y-1\right)\left(y+6\right)} times \frac{y-4}{y-4}.
\frac{\left(4y+9\right)\left(y-1\right)+7\left(y-4\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
Since \frac{\left(4y+9\right)\left(y-1\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)} and \frac{7\left(y-4\right)}{\left(y-4\right)\left(y-1\right)\left(y+6\right)} have the same denominator, add them by adding their numerators.
\frac{4y^{2}-4y+9y-9+7y-28}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
Do the multiplications in \left(4y+9\right)\left(y-1\right)+7\left(y-4\right).
\frac{4y^{2}+12y-37}{\left(y-4\right)\left(y-1\right)\left(y+6\right)}
Combine like terms in 4y^{2}-4y+9y-9+7y-28.
\frac{4y^{2}+12y-37}{y^{3}+y^{2}-26y+24}
Expand \left(y-4\right)\left(y-1\right)\left(y+6\right).