Question

How do you simplify `\frac { 2} { y } + \frac { 5} { y + 4} - \frac { 3} { y ^ { 2} }`?

Answer 1

`2/y+5/(y+4)-3/(y^2)=color(red)((7y^2+5y-12)/(y^3+4y^2))`

Explanation:

Replacing `y^2` with `(color(magenta)y)(color(blue)y)`#

`2/y+5/(y+4)-3/(y^2)`

becomes:
`2/color(magenta)y+5/(color(lime)(y+4))-3/((color(magenta)y)(color(blue)(y))`

`color(white)("XXX")=(2(color(blue)y)(color(lime)(y+4))+5(color(magenta)y)(color(blue)y)-3(color(lime)(y+4)))/((color(magenta)y)(color(blue)y)(color(lime)(y+4)))`

`color(white)("XXX")=(2y^2+8y+5y^2-3y-12)/(y^3+4y^2)`

`color(white)("XXX")=(7y^2+5y-12)/(y^3+4y^2)`