Math Is Fun Forum

Can the following fraction be simplified further?
Numerator;   2(x+3)
Denominator; 2(x+1)

Does anybody else hate these?

Is it just me, or are they messy/awkward/UGLY/unsatisfying?

I came across the following inequality in this context;

x ≤ 6-2y

My instinct was to rearrange it to have y on the left hand side thus;

y ≤ -(1/2x) +3

Should I have bothered?

I guess I'm used to seeing it that way.

I simplified an algebraic fraction to; 4x+6/(x-3)

But the answer given was 2(2x+3)/(x-3)

They hadn't expanded 2(2x+3) to 4x+6

Did I go too far, or did they not go far enough?

Is the planet (Earth) dying?
Was it ever alive?
Before the first soil, before the first moss, or moss-like plant, or blue-green algae - basically before the first life forms that would attach themselves to the surface of the Earth, what was the surface like?
Was it smooth, like an enormous (almost) spherical stone? What was it’s composition, approximately?
And, back to the top, if every life form on Earth went extinct and all the corpses (including the plant ‘corpses’) decomposed, to dust (?) would the planet be just as it was 4-5 billion years ago before life arose on it?

Surface Area
If the surface area of solid shape is 4cm^2 what can we infer about the shape?
Not a sphere (pi would lead to decimals)?
Same for cones and cylinders?
Pyramid?
Or does 4cm^2 have a square ‘ring’ to it? Should we be thinking cube/cuboid?

Also, at GCSE level (UK), or at any level for that matter, does 'solid shape' refer to 'straightforward' solid shapes, as opposed to the 3d versions of compound shapes?