Solve the equation for x. -1+((2x)/(x+3))=((-2)/(x+2))

- anonymous

Solve the equation for x. -1+((2x)/(x+3))=((-2)/(x+2))

- katieb

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- anonymous

Multiply the equation by the LCD.

- anonymous

Sorry I should have stated to solve the equation for x.

- anonymous

K, let's start again.....

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## More answers

- anonymous

okay

- anonymous

What is it u want to do?

- anonymous

|dw:1350674953315:dw|

- anonymous

Yes, so what is it u want to do?

- anonymous

Multiply (-1), (2x/x+3), and (-2x/x+2) by the LCD of (x+3) and (x+2).

- anonymous

OK, that is the long way around of solving for x.
You will get to the same place at the end.
I guess your teacher has told u to do it that way, right?

- anonymous

yes

- anonymous

LCD of (x+3) and (x+2) is just (x+3)(x+2)
I will leave you to it, it is not too hard to do.

- anonymous

Okay. Thank you. I know the answer is (-1,0). I just wanted to make sure I was on the right path.

- anonymous

U should also note that x=-3 and x = -2 are not defined for this equation.

- anonymous

correct

- anonymous

Could you please explain the shorter way of doing this type of equation.

- anonymous

If you add the terms on the left side -> (x-3)/(x+3) = -2/(x+2)
Cross multiply -> (x-3)(x+2) = -2(x+3) ->
x^2 -x -6 = -2x - 6 -> x^2 + x = 0 -> x( x +1) = 0 -> x = 0 or -1

- anonymous

Wow that is much quicker! Thank you so much

- anonymous

yw:)

- anonymous

The other way reminds you that the original equation is not defined for x=-3 and x = -2
But with some practice you will not need reminding....

- anonymous

Could I use this shorter way for this equation as well? (see drawing)

- anonymous

|dw:1350677688912:dw|

- anonymous

Yes, u can.

- anonymous

Thanks. When I add the terms on the LHS I get (z+1) / (z-6). Is this correct?

- anonymous

No, (z+1) + 1*(z-6) / (z-6) = (2z-5) / (z-6)

- anonymous

Gotcha. Thanks

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