How do you simplify y/(2y)+ (y+2)/yy2y+y+2y?

2 Answers
Jun 14, 2018

y/[2y] + [y+2]/yy2y+y+2y

=[y+2(y+2)]/[2y]=y+2(y+2)2y

=[y+2y+4]/[2y]=y+2y+42y

=[3y+4]/[2y]=3y+42y

Jun 14, 2018

\frac{3y+4}{2y}3y+42y

Explanation:

If you multiply and divide by 22 the second fraction we get

\frac{y}{2y}+\frac{2(y+2)}{2y} = \frac{y+2(y+2)}{2y} = \frac{y+2y+4}{2y}=\frac{3y+4}{2y}y2y+2(y+2)2y=y+2(y+2)2y=y+2y+42y=3y+42y

If you prefer, you can break the fraction in two fraction by writing

\frac{3y+4}{2y} = \frac{3cancel(y)}{2cancel(y)}+\frac{cancel(4)^2}{cancel(2)y} = \frac{3}[2}+\frac{2}{y}.

It depends on your idea of "simplifying", as far as I know there is no standard definition for that term. Let me know if I'm wrong!