Posted by **Bart** on Thursday, January 10, 2013 at 1:44pm.

I know the answer to this problem is -1. I found that by substituting for x and seeing if it worked. How should I do it the correct way?

(x/(3x+6))-(x+1/3x-6)=(1/(x^2)-4)

- Algebra 2 -
**Steve**, Thursday, January 10, 2013 at 2:06pm
first, use enough parens to be correct:

(x/(3x+6))-(x+1)/(3x-6)=(1/(x^2)-4)

factor out the 1/3 on the left side, and factor the right side

1/3 (x/(x+2) - (x+1)/(x-2)) = 1/((x+2)(x-2))

now put LS over a common denominator

1/3 (x(x-2) - (x+1)(x+2))/((x-2)(x+2)) = 1/((x+2)(x-2))

multiply through by 3(x-2)(x+2)

x(x-2) - (x+1)(x+2) = 3

x^2 - 2x - x^2 - 3x - 2 = 3

-5x - 2 = 3

-5x = 5

x = 1

- Algebra 2 -
**Bart**, Thursday, January 10, 2013 at 3:24pm
Thank you for your help. I still need some more explaining. I understand factoring out the 1/3 on the left hand side. I also understand factoring the denominator on the right hand side. After that I have trouble. Could you please show it to me again, but this time with more steps shown?

- Algebra 2 -
**Steve**, Thursday, January 10, 2013 at 5:40pm
If you are ok to here:

1/3 (x/(x+2) - (x+1)/(x-2)) = 1/((x+2)(x-2))

Think of it as something like

1/3 (3/5 - 4/7) = 1/(35)

To clear the fractions, multiply by the LCD of them all: 3*5*7 = 35

In our case, 3(x+2)(x-2)

1/3 x/(x+2) * 3*(x-2)(x+2) --> x(x-2)

the other factors cancel out. Do that for all three terms of the equation and you get to the next step, which is much easier to read:

x(x-2) - (x+1)(x+2) = 3

and from there it should be clear. That help?

## Answer this Question

## Related Questions

- Algebra 2 - I know the answer to this question is: -1. I got that answer by ...
- CHEMISTRY HELP PLEASE - when I use henderson-hasselbach Ka of HOP4^2- = 4.8 x10...
- methods of sbtracting mixed fractions - Hello, I need did a subtraction problem ...
- algebra - i have two answers to this problem so am not sure which way I need to ...
- equations - solve for x and y x+y=5 and x^x + y^y = 31 i have found x,y = 2,3 or...
- Calculus again - Find the equation of the tangent to y=2-xe^x at the point where...
- algebra - f(x)=2x+5, find f(3) would this be worked out liek this 2(3)+5=11 Your...
- To Laura/Joseph - I have taken care of the answer to the SO3 ==> SO2 + O2 ...
- Math Question - Hi! We asked this question last night but we got confused. Find ...
- Algebra 2 - Find the inverse of the following function: f(x) = 3x + 12 I don't ...