Question

2y2 + 9y-5
4y2 - 1
сократите дробь

Answer 1

$2y^2+9y-5=0$
$D=9^2-4*2*(-5)=81+40=121=11^2$
$y_1=frac{-9-11}{2*2}=-5$
$y_2=frac{-9+11}{2*2}=frac{1}{2}$
$2y^2+9y-5=2(y-frac{1}{2})(y-(-5))=(2y-1)(y+5)$
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$4y^2-1=(2y)^2-1^2=(2y-1)(2y+1)$
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$frac{2y^2+9y-5}{4y^2-1}=\\frac{(2y-1)(y+5)}{(2y-1)(2y+1)}=\\frac{y+5}{2y+1}$