Homework Help

Simplify the expressions and solve the equations.

user profile pic

anya4one | Student, Undergraduate | Honors

Posted July 22, 2013 at 7:21 PM via web

dislike 2 like

Simplify the expressions and solve the equations.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

1 Answer | Add Yours

user profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 22, 2013 at 7:41 PM (Answer #1)

dislike 2 like

(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:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes