Question

What is the sum? 3y/y^2+7y+10 + 2/y+2

Answer 1

Hello mate.

Thanks for asking this useful question

$So\:your\:answer\:is=>$

Our given equation is =>


$=> \boxed {\frac{3y}{y^{2}+7y+10}+ \frac{2}{y+2}}$


Let our final summation be "x"


$=> \boxed { \frac{3y}{y^{2}+7y+10}+ \frac{2}{y+2}\:=\:x}$


taking LCM on LHS ,


$=> \frac {3y(y+2)+2(y^{2}+7y+10)}{(y+2)(y^{2}+7y+10 )}\:=\:x$


$=> \frac{3y^{2}+6y+2y^{2}+14y+20}{(y+2)(y^{2}+7y+10)}\:=\:x$


By solving and using factorisation method on denominator side ;


$=> \frac {5y^{2}+20y+20}{(y+2)[(y+2)(y+5)]}\:=\:x$


$=> \frac{5(y^{2}+4y+4)}{(y+2)(y+2)(y+5)}\:=\:x$


by using factorisation method on nominator side ,


$=> \frac {5[(y+2)(y+2)]}{(y+2)(y+2)(y+5)}\:=\:x$


$=>\frac {5( {\cancel {(y+2) (y+2)})}}{ {\cancel {(y+2) (y+2)}} (y+5)}\:=\:x$


$=>\boxed { \frac{5}{y+5}\:=\:x}$


So our final equation is ,


$\boxed {\frac {3y}{y^{2}+7y+10}+ \frac {2}{y+2} \:=\: \frac {5}{y+5}}$



Hope u understood ^_^



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