Simplify and state any restrictions on the variables.

Question

anonymous · Answer

$${6x \over x ^{2}-5x+6}- {3x \over x ^{2}+x-12}$$

anonymous · Answer

Please also express your process as to how you got the restrictions.

btaylor · Answer

To simplify:
Factor the denominators, then figure out what you need to do to make both equations equal.
So: $$[\frac{(x+4)(x-3)}{(x+4)(x-3)} \times \frac{6x}{(x-6)(x+1)}] - [\frac{(x-6)(x+1)}{(x-6)(x+1)} \times \frac{3x}{(x+4)(x-3)}]$$
So you multiply out all the numerators, and then subtract them. Then simplify.

For the restrictions: Whatever is in the denominator cannot be zero, or the function will be undefined. So take the factors (x-6) , (x+1) , (x+4) , (x-3) and set them equal to zero, then solve for x. So x cannot be 6, -1, -4, or 3.

anonymous · Answer

You factored incorrectly above @BTaylor . x^2 - 5x + 6 = (x-2)(x-3) not (x-6)(x+1)

ajprincess · Answer

@BTaylor the factors of x^2-5x+6 are (x-3) and (x-2)

btaylor · Answer

oh. my bad.

anonymous · Answer

So what would be the new restrictions?

anonymous · Answer

I believe they would be: \[x \not= 2,3,-4\
Am I correct?

btaylor · Answer

@genius12 your restrictions are correct

anonymous · Answer

Ok then. Thanks for help.