x/(2x-4)-7=1/(x-2)..

Question

How I clear this denominator if I must clear it at all.. Im not sure how to approach these problems.I have several others similar to this

1/2y+ 4= 1/7y
I changed the denominators to 14y, then got 7/14y+ 4= 2/7y but my online homework says that is incorrect.

5/8x + 2/7 = -2/7x+ 3/8

and also 3/(x-4)=7/(x-8)..PLEASE HELP ME PLEASEEEEEEEEEE, I have been stuck for hours a just don't know how to approach these problems

Answer 1

The common denominator is 2(x-2). If you multiply through by that, you get

x - 7*2(x-2) = 1*2
Now just proceed normally:
x - 14x + 28 = 2
-13x = -26
x = 2

For the next one, you must be interpreting the equation as

1/(2y) + 4 = 1/(7y)

if you multiply by 14y, you get

y + 4*14y = 2
y+56y = 2
y = 2/57

If, as I suspect, the equation is really

(1/2)y + 4 = (1/7)y, then you just have a LCD of 14, not 14y. Clear that and you get

7y + 4*14 = 2y
-5y = 56
y = -56/5

I see no advantage in either interpretation, except for choosing the right one!

(5/8)x + 2/7 = (-2/7)x + 3/8
With a LCD of 56, you get

35x + 2*8 = -16x + 21
51x = 5
x = 5/51

Answer 2

Your last one
3/(x-4)=7/(x-8)
is the easiest of the three equations

just multiply each side by (x-4)(x-8) , which is sometimes called "cross-multiplying"

7(x-4) = 3(x-8)
7x - 28 = 3x - 24
4x = 4
x = 1