Answer:
[tex]\frac{y-2}{4}[/tex]
Step-by-step explanation:
Let's start by factoring everything:
[tex]\dfrac{\frac{y^2+y}{y^2-2y}}{\frac{4y+4}{y^2-4y+4}}=[/tex]
[tex]\dfrac{\frac{y(y+1)}{y(y-2)}}{\frac{4(y+1)}{(y-2)^2}}=[/tex]
Now, you can cancel out some terms:
[tex]\dfrac{\frac{y+1}{y-2}}{\frac{4(y+1)}{(y-2)^2}}=[/tex]
Now, when you divide a fraction by another fraction, that is the same as multiplying the first fraction by the reciprocal of the second one:
[tex]\frac{y+1}{y-2}\cdot \frac{(y-2)^2)}{4(y+1)}=[/tex]
[tex]\frac{y-2}{4}[/tex]
Hope this helps!
