Homework Help

Find all real solutions to the equation 1 - 1/(x-2) = -4/(x^2-4).

user profile pic

clara2 | Student, Undergraduate | eNoter

Posted January 17, 2011 at 10:25 AM via web

dislike 0 like

Find all real solutions to the equation 1 - 1/(x-2) = -4/(x^2-4).

Tagged with math

1 Answer | Add Yours

user profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted January 17, 2011 at 10:31 AM (Answer #1)

dislike 0 like

1 - 1/(x-2) = -4/(x^2 - 4)

First we will rewrite 1 as a fraction.

==> 1 = (x-2)/(x-2)

==> (x-2)/(x-2) - 1/(x-2) = -4/(x^2 -4)

==> (x-2-1)/(x-2) = -4/(x^2-4)

==> (x-3)/(x-2) = -4/(x^2 -4)

Now we will factor x^2 -4 = (x-2)(x+2)

==> (x-3)/(x-2) = -4/(x-2)(x+2)

Now we will reduce similar terms.

==> (x-3) = -4/(x+2)

Now we will multiply by (x+2).

==> (x-3)(x+2) = -4

==> x^2 -x - 6 = -4

==> x^2 -x -2 = 0

==> (x-2)(x+1) = 0

==> x = 2 and x= -1

==> x = ( -1, 2}

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes