how to simplify   x^2+3x+2/x+2 find restrictions and simplfy.......... next problem......   find the LCD on both of these   5/6x^2y - 7/6xy^3 and then simplify.have to show work on both...

how to simplify   x^2+3x+2/x+2 find restrictions and simplfy.......... next problem......   find the LCD on both of these   5/6x^2y - 7/6xy^3 and then simplify.

have to show work on both problems......Thank you so very much

embizze | Certified Educator

(1) Simplify `(x^2+3x+2)/(x+2)` :

`(x^2+3x+2)/(x+2)=((x+2)(x+1))/(x+2)` Factor the numerator

`=x+1` Cancel the common term

Thus `(x^2+3x+2)/(x+2)=x+1` for `x!=-2` (Note that the restriction is required as x=-2 is not in the domain of the given expression)

(2) Simplify `5/(6 x^2y)-7/(6xy^3)` :

First we find the least common denominator:

`6x^2y=2*3*x*x*y`

`6xy^3=2*3*x*y*y*y`

To find the least common denominator we find the product of the common factors as well as the factors not in common; here the LCD is `2*3*x*y*x*y*y=6x^2y^3` (A simple way is to find the LCM of the numeric part, and then keep the highest power of each variable)

To simplify we add the fractions:

`5/(6x^2y)-7/(6xy^3)=(5y^2)/(6x^2y^3)-(7x)/(6x^2y^3)`

`=(5y^2-7x)/(6x^2y^3)`