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

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lemjay's profile pic

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

Posted on

`(x+4)/x=-5`

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

`x*((x+4)/x)=-5*x`

`x+4=-5x`

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

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

`4=-6x`

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

`4/(-6)=(-6x)/(-6)`

`-2/3=x`

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

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

oldnick's profile pic

oldnick | (Level 1) Valedictorian

Posted on

`8/[(x-9)(x-1)]-1/(x-1)=1/(4x-36)`

rewriting:

 

`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`

developing:

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

`-4x - 4= x -1`

adding 4x both sides:

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

So:

`-4 =5x-1`

adding 1 both sides:

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

So that:

`-3=5x`

Mdividing both sides by 5:

`-3/5=5x/5`

that shows the solution:

`x=-3/5`

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