Answer:
[tex]\frac{2y^2-5y-7}{6y^2+10y+4}-\frac{7}{9y^2+6y}=\frac{6y^2-21y-14}{6y\left(3y+2\right)}[/tex]
Step-by-step explanation:
we are given
[tex]\frac{2y^2-5y-7}{6y^2+10y+4}-\frac{7}{9y^2+6y}[/tex]
we have to simplify it
Firstly, we will factor it
[tex]2y^2-5y-7=\left(y+1\right)\left(2y-7\right)[/tex]
[tex]6y^2+10y+4=2\left(y+1\right)\left(3y+2\right)[/tex]
[tex]9y^2+6y=3y(3y+2)[/tex]
[tex]=\frac{\left(y+1\right)\left(2y-7\right)}{2\left(y+1\right)\left(3y+2\right)}-\frac{7}{3y(3y+2)}[/tex]
now, we can cancel like terms
[tex]=\frac{\left(2y-7\right)}{2\left(3y+2\right)}-\frac{7}{3y(3y+2)}[/tex]
now, we can combine it
[tex]=\frac{3y(2y-7\right)}{6y\left(3y+2\right)}-\frac{7\times 2}{6y(3y+2)}[/tex]
[tex]=\frac{3y(2y-7\right)-14}{6y\left(3y+2\right)}[/tex]
[tex]=\frac{6y^2-21y-14}{6y\left(3y+2\right)}[/tex]
so, we get
[tex]=\frac{6y^2-21y-14}{6y\left(3y+2\right)}[/tex]
