7/x-3 - 1/2 = 3/x-4?

Question

This is an equation with radical expressions (fractions). I've tried solving it several times and keep getting -13, -2. I only have these choices though: -5, 5, 15, 10, 12, 25, -10. I know to take the LCD and distribute it, and the LCD is (x-3)(x-4) but how do I keep getting the wrong answer? Thanks for any suggestions/explanations you have!

Answer 1

The answer is 5 and 10. Don't try and solve it, just plug 5 and 10 in and you'll see they work. :) I actually tried solving it the way you did, and got the wrong answers twice too. Finally after getting my signs correct I got it.

7/(x-3) - 1/2 = 3/(x-4)

I moved 1/2 over for no reason

7/(x-3) = 3/(x-4) + 1/2

7/(x-3) = 6/2(x-4) + (x-4)/2(x-4)

7/(x-3) = (x+2)/2(x-4)

14(x-4) = (x+2)(x-3)

14x - 56 = x^2 - x - 6

x^2 - 15x + 50 = 0

(x - 5)(x - 10) = 0

wow, it's been a while since i've done one of these

Answer 2

Step by step :)
7/x-3 - 1/2 = 3/x-4

multiply by LCD (I'm using 2(x-3)(x-4) to make it simpler, although you could use your one you'd get the same answer):

14(x-4) - (x-3)(x-4) = 6(x-3)
14x -56 - x^2 - 12 + 7x = 6x -18
-x^2 +15x - 50 = 0
A quadratic equation :D ...
either use the quadratic formula, or the factors of this are:
(-x + 10)(x-5)= 0
so at least ONE of those most equal zero
if -x -10 = 0 then x = - 10
if x - 5 = 0 then x = 5

SO THERE ARE TWO!!! answers are 5, and - 10

Check them, they both work :) !!

Answer 3

7 / (x - 3) - 1 / 2 = 3 / (x - 4)
14 (x - 4) - (x - 3)(x - 4) = 6 (x - 3)
14x - 56 - (x² - 7x + 12) = 6x - 18
14x - 56 - x² + 7x - 12 = 6x - 18
21x - 68 - x² = 6x - 18
x² - 15x + 50 = 0
(x - 10) (x - 5) = 0
x = 5 , x = 10

Answer 4

(7/x-3) - 1/2 = 3/x-4

(7/x-3) - (3/x-4) = 1/2

(7x-28-3x+9)/[(x-3)(x-4)] = 1/2

(4x-19)/[(x-3)(x-4)] = 1/2

8x - 38 = x^2 - 4x - 3x + 12

x^2 - 15x + 50 = 0
(x - 5) ( x - 10) = 0

x = 5, x = 10.

Answer 5

i have done your answer on my sheet butving i m also having problems..

my advice to you is to rearrange the equations and solve for x