I'm doing rational equations. Having trouble with a couple. Was hoping to get the steps for these examples. (1) `(x+4)/x=-5`   (2) 8/(x-9)(x-1)-1/x-1=1/4x-36

2 Answers

lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on


To solve rational equations, we need to multiply it by the LCD. In the given problem, the LCD is x.



Then, bring together the terms with x on one side of the equation. So, subtract both sides by x.



And, to get x only at the right side of the equation, divide both sides by -6.



Hence, the solution to the given equation is `x=-2/3` .

(For problem #2, please post it as separate question in Homework Help.)

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oldnick | (Level 1) Valedictorian

Posted on




`8/[(x-9)(x-1)]-1/(x-1)= 1/[4(x - 9)]`

moltiplyng bot sides: `4(x -9)(x-1)` we get:


`[32(x-9)(x-1)]/[(x-9)(x-1)]- 4[(x-9)(x-1)]/[(x-1)]=[4(x-9)(x-1)]/[4(x-9)]`

`32-4(x - 9)=x -1`


`32- 4x-36= x-1`

`-4x - 4= x -1`

adding 4x both sides:



`-4 =5x-1`

adding 1 both sides:

`-4 +1= 5x -1 +1`

So that:


Mdividing both sides by 5:


that shows the solution: