Question

Okay, I am adding rational expressions (and stating restrictions) and I've done this so far:

-3x/x^2-9 + 4/2x-6
-3x/(x+3)(x-3) + 4/2(x-3)

I'm not sure where to go from here, looking for help not a "the answer is 2x^2*3" without an explanation

Answer 1

\[=\frac{-6x+4(x+3) }{ 2\left( x+3 \right)\left( x-3 \right) }=?\]

Answer 2

I have no idea.... not really grasping this atm.

Answer 3

Oh oh, if you were asking me what that equaled gimme a sec

Answer 4

I actually need to leave for a bit, eating dinner

Answer 5

\[=\frac{ -2x+12 }{ 2\left( x+3 \right)\left( x-3 \right) }=\frac{ -x+6 }{\left( x+3 \right)\left( x-3 \right) }\]

Answer 6

Okay I'm not getting how it's getting from:
\[\frac{ -3x }{ (x+3)(x-3) } + \frac{ 4 }{ 2(x-3) }\]
to:
\[\frac{ -6x+4(x+3) }{ 2(x+3)(x-2) }\]

Answer 7

\[\frac{ -3x }{\left( x+3 \right)\left( x-3 \right) }+\frac{ 4 }{2\left( x-3 \right) }=\frac{-3x }{\left( x+3 \right)\left( x-3 \right) }+\frac{ 2 }{x-3 }\]
\[=\frac{ -3x+2\left( x+3 \right) }{\left( x+3 \right)\left( x-3 \right) }=\frac{ -x+6 }{ \left( x+3 \right)\left( x-3 \right) }\]

Answer 8

Okay, so.... no idea how you got that...

Answer 9

Part of the difficulty here may stem from our trying to interpret your two rational expressions as fractions. Surjithayer has tried doing that, using the Equation Editor. I strongly encourage you to learn how to use that to your benefit.

Next, I understand that you have two rational expressions and you want to add them / combine them. Remember that we can't add fractions unless the denominators are the same?

So I'd look carefully at the denominators of each of your expressions below and ensure that they are the same before I'd try to combine the fractions. If the denoms differ from one another, we'll have to find the LCD (least common denom.) and modify each fraction, if necessary, to obtain fractions with the same denominators.

Once you reach that point the rest is pretty straightforward.

Questions?

Answer 10

-3x/x^2-9 + 4/2x-6
-3x/(x+3)(x-3) + 4/2(x-3)

My interpretation of -3x/x^2-9 + 4/2x-6 follows:

\[\frac{ -3x }{ x ^{2} -9}+\frac{ 4 }{ 2x-6 }\]

Answer 11

That is correct for the first bit, should've done it as an equation.

Answer 12

My main issue is that I'm stuck at the step of finding the LCD.
Do I just multiply the top and bottom by it i.e.
\[\frac{ -3x(x+3)(x-3) }{ (x+3)(x-3)(x+3)(x-3) }\]

Answer 13

The next step is to determine what the LCD is. To do that, factor both denoms.:
\[\frac{ -3x }{ (x-3)(x+3) }+\frac{ 4 }{ (2)(x-3)}\]

You can either figure out the LCD yourself or take my word for it: If we don't reduce the 2nd fraction, then the LCD is 2(x-3)(x+3). If we DO reduce the 2nd fraction, then the LCD is (x-3)(x+3).

Can you take the addition from here? Remember: your fractions MUST have the same denom. before you can add them.

Answer 14

Or \[\frac{ -3x }{ (x+3)(x-3) } * \frac{ (x+3)(x-3) }{ (x+3)(x-3) }\]

Answer 15

OK: Let's focus on that LCD business:

\[\frac{ -3x }{ (x-3)(x+3) }+\frac{ 2 }{ (x-3)}\] is what we have after simplifying the 2nd fraction (see above).

The LCD is (x-3)(x+3). The left fraction already has that LCD; the right one will have the LCD if you multiply both its numerator and denom. by (x+3).

\[\frac{ -3x }{ (x-3)(x+3) }+\frac{ 2(x+3) }{ (x-3)(x+3)}\]
With the denoms now equal, the rest is a snap. Combine the numerators:

-3x + 2x + 6

and write the result in the numerator of the final answer and (x+3)(x-3) in the denominator. Lo and behold, we're then done!

Answer 16

Please compare your approach and my approach. What can you learn from that?

Answer 17

Well for one I really had no idea what I was doing, but with what you said I think I get this. Gonna write it out and see if I really get it.

Answer 18

While I'm disconnecting very soon, I'd be happy to hear back from you again regarding this or other questions. Either reply here or send me a message through OpenStudy. Good luck!