Please help me isolate x
(x-a)/b-(x+c)/d=0
Do you mean $\displaystyle \displaystyle \frac{(x - a)}{b} - \frac{(x - c)}{d} = 0$?
If so...
$\displaystyle \displaystyle \begin{align*} \frac{(x - a)}{b} - \frac{(x - c)}{d} &= 0 \\ \frac{(x - a)}{b} &= \frac{(x - c)}{d} \\ d(x - a) &= b(x - c) \end{align*}$
Now expand the brackets and see what you can do from there...
Your maths book would be right
As Prove It says (with the amended $\displaystyle (x+c)$:
$\displaystyle [(x-a)/b]-[(x+c)/d]=0$
add $\displaystyle (x+c)/d$ to both sides
$\displaystyle (x-a)/b=(x+c)/d$
multiply top and bottom of lhs by $\displaystyle d$
multiply top and bottom of rhs by $\displaystyle b$
gives
$\displaystyle d(x-a)/bd=b(x+c)/bd$
multiplying both sides by $\displaystyle bd$ gives
$\displaystyle d(x-a)=b(x+c)$
You should be able to complete it from there
hth
btw Prove It, How do you get the horizontal line for divide?
thx
Pro
You're getting theredx-bx=ad+bc, then divide both sides with d-b?
$\displaystyle dx-bx=ad+bc$
$\displaystyle dx-bx$ is the same as $\displaystyle x(d-b)$
so we have x(d-b)=(ad+bc)
dividing both sides by (d-b) gives
$\displaystyle x=(ad+bc)/(d-b)$