(x)/(x-2) - (x+1)/(x) = (8)/(x^2-2x)
I keep getting x = 6
can someone show me how you guys are getting x = -10
The lowest commond denominator is x(x-2)
x/x *(x)/(x-2) - (x+1)/(x) *(x-2)/(x-2)=(8)/x(x-2)
multiplying both sides by the common denominator..
x^2 -(x^2-1x -2)=8
x+2=8
x=6
check
6/4 - 7/6=8/24
36/24 - 28/24=
8/24=8/24
it checks.
OK, here's how I would go about this problem:
(x)/(x-2) - (x+1)/(x) = (8)/(x^2-2x)
(x)/(x-2) - (x+1)/(x) = (8)/x(x-2) -->factoring the denominator (x^2-2x).
Common denominator is: x(x-2)
Multiply every term by the common denominator to get rid of the fractions and make the equation easier to solve.
x(x-2) [(x)/(x-2) - (x+1)/(x) = (8)/x(x-2)]
x^2 - (x+1)(x-2) = 8
x^2 - (x^2 - x - 2) = 8
x^2 - x^2 + x + 2 = 8
x + 2 = 8
x = 6
Substitute 6 for x in the original equation. It always helps to check your work!
I hope this is clear and will help.
you get the same answer as i do but others are saying here someone named annonimous that they keep getting -10.
It seems there might be some confusion or error in the calculations done by an anonymous user if they are getting -10 as the answer. However, it's possible that they took a different approach or made a mistake. It's also important to note that sometimes equations can have multiple solutions.
To verify which answer is correct, you can substitute both x = 6 and x = -10 back into the original equation and see if they satisfy it.
For x = 6:
(x)/(x-2) - (x+1)/(x) = (8)/(x^2-2x)
(6)/(6-2) - (6+1)/(6) = (8)/(6^2-2*6)
6/4 - 7/6 = 8/24
36/24 - 28/24 = 8/24
8/24 = 8/24
So, x = 6 is indeed a valid solution.
For x = -10:
(-10)/(-10-2) - (-10+1)/(-10) = (8)/(-10^2-2*(-10))
(-10)/(-12) - (-9)/(-10) = (8)/(100+20)
5/6 - 9/10 = 8/120
50/60 - 54/60 = 8/120
-4/60 = 8/120
-1/15 = 8/120
As you can see, it does not satisfy the equation. Therefore, x = -10 is not a valid solution.
Hence, based on these calculations, x = 6 is the correct solution.