Need help with this equation(s)

[Ariselea]

I'd love to go to University in the next few years, but first, clear myself of debt and do a bridging course in mathematics, physics and chemistry.
Before I do these courses, I thought I'd brush up on some maths first (I dropped out after year 10 to do my apprenticeship - dumb as bat shit).

Year 11 Maths B:

This equation is messing with my mind.

x/a + x/b = 1

I don't have a teacher to check with so could anyone please check my other equations I attempted before?
*brackets after the equation is the step I did*

a) ax + b = 0 (-b)
= ax = 0 - b (/a)
x = -b/a

b) cx + d = e (-d)
= cx = e - d (/c)
x = (e - d)/c

c) a(x+b) = c (/a)
= x+b = c/a (-b)
x = c/a - b

d) ax - b = cx (+b)
= ax = cx + b (-cx)
= ax - cx = b
= (a - c)x = b (/ (a-c))
x = b/(a-c)

[Deleted]

a, b, c and d) are all correct.

For the other:
x/a+x/b=1
*a
x+ax/b = a
*b
bx+ax = ab
(b+a)x = ab
/(b+a)
x = ab/(b+a)

[Independent voter]

Wolfram Alpha says

x(-a -b) = -ab

among many other things

[kreationkin]

x/a + x/b = 1

(factor out x)

x (1/a + 1/b) = 1

(divide by 1/a + 1/b)

x = 1 / (1/a + 1/b) or = ab / (a+b) (alternate form of same equation as seen in Starquake's post)

[Ariselea]

a, b, c and d) are all correct.

For the other:
x/a+x/b=1
*a
x+ax/b = a
*b
bx+ax = ab
(b+a)x = ab
/(b+a)
x = ab/(b+a)

Thank you very much

It plays a bit of havoc on my mind when I don't see the numbers, just pronumerals (they are pronumerals right?!). I just started linear equations the other day from some grubby old text book my sister had lying around.
I've only got examples shown in there to go from.

[Deleted]

what aren t this in 8th grade