Perform the indicated operations, then simplify. (5y)/(y+10)+(8y^2)/(y^2)-100-(9)/(y-10) (13y^2-59y-90)/((y+10)(y-10)) (8y^2+5y-9)/((y+10)(y-10)) (8y^2+5y-9)/(y^2)+2y-100 (13y^2-59y+90)/((y-10)(y+10))

To simplify the given expression, we need to perform the indicated operations and then simplify the resulting expression.<br /><br />The given expression is:<br />$\frac {5y}{y+10}+\frac {8y^{2}}{y^{2}-100}-\frac {9}{y-10}$<br /><br />Step 1: Find a common denominator for the fractions.<br />The common denominator is $(y+10)(y-10)$.<br /><br />Step 2: Rewrite each fraction with the common denominator.<br />$\frac {5y}{y+10} = \frac {5y(y-10)}{(y+10)(y-10)}$<br />$\frac {8y^{2}}{y^{2}-100} = \frac {8y^{2}}{(y+10)(y-10)}$<br />$\frac {9}{y-10} = \frac {9(y+10)}{(y+10)(y-10)}$<br /><br />Step 3: Combine the fractions.<br />$\frac {5y(y-10)}{(y+10)(y-10)} + \frac {8y^{2}}{(y+10)(y-10)} - \frac {9(y+10)}{(y+10)(y-10)}$<br /><br />Step 4: Simplify the numerator.<br />$5y(y-10) + 8y^{2} - 9(y+10)$<br />$= 5y^2 - 50y + 8y^2 - 9y - 90$<br />$= 13y^2 - 59y - 90$<br /><br />Step 5: Write the final simplified expression.<br />$\frac {13y^{2}-59y-90}{(y+10)(y-10)}$<br /><br />Therefore, the simplified expression is $\frac {13y^{2}-59y-90}{(y+10)(y-10)}$.