# Simplify the expressions and solve the equations.

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(1) Simplify `(v^2+v-12)/(v^2+6v+8) -:(2v-6)/(v+2)` Factor each term:

`((v+4)(v-3))/((v+4)(v+2))-: (2(v-3))/(v+2)` Divide is the same as multiply by reciprocal

`((v+4)(v-3))/((v+4)(v+2))*(v+2)/(2(v-3))` Use the multiplicative identity to reduce common factors in the numerator and denominator (i.e. cancel common factors):

`1/2`

**So the expression simplifies to `1/2` **

(2) Solve `2/(b-2)=b/(b^2-3b+2)+b/(2b-2)`

`2/(b-2)=b/((b-2)(b-1))+b/(2(b-1))`

The least common denominator is `2(b-1)(b-2)` -- multiply everything by the LCD to get:

`2(2)(b-1)=b(2)+b(b-2)`

`4b-4=2b+b^2-2b`

`b^2-4b+4=0`

`(b-2)^2=0`

`==> b=2`

However, if b=2 then the left side of the original equation is undefined, so b=2 will not work.

**There is no solution to the equation.**

Here is the graph of the left side in red, and the right side in blue. Any solution would be where the graphs intersect: