Subtract x / x - 4 by 2x / (x -5)

Question

anonymous · Answer

I'm getting stuck on this one when simplifying...:/

demandandsupply · Answer

Ok

demandandsupply · Answer

So you need the same denominators. to do this, times x/x-4 by x-5, that is top and bottom but do not simplify at this stage. similarly,  times 2x/x-5, top and bottom, by x-4

anonymous · Answer

Yeah, I know the denominator is (x -4) (x - 5), but with the numerator, I start having 
x(x - 5) - 2x(x - 4) and then x^2 - 5x - 2x^2 + 8x 
but how do I go from here?

demandandsupply · Answer

Ok that seems correct, from there i simplified it to -x^2 +3x on top

demandandsupply · Answer

From there, there isnt really alot you can do. You can divide top and bottom by -1 to remove -x^2. that would give x^2 - 3x / (4+x)((5+x)

anonymous · Answer

Ok, thanks so much for explaining! I don't think I'm supposed to remove the negative sign though, is it usually necessary?

demandandsupply · Answer

No problem, typically in maths we just try and make things look a little neater, but it is still the correct answer