x/2-x/x-4=-4/x-4=-4x^2/2
check this please
Please check your typing, and use brackets to avoid ambiguity.
in the problem there are no brackets
x over x minus x/over x-4 equal -4 over x-4 solve each rational equation if it has no equation state so. simply with necessary
Please help me
So it is
[x/(2-x)]/(x-4) = -4/(x-4) ?
Where does the third equality come from ?
Can you see why brackets are absolutely necessary here?
ok, first multiply both sides by x-4 to get
x/(2-x) = -4
now multiply both sides by 2-x
x = -4(2-x)
x = -8 + 4x
-3x = -8
x = 8/3
Lastly, what does "...if it has no equation state so. simply with necessary " mean ?
To check whether x/2 - x/(x-4) = -4/(x-4) = -4x^2/2, we need to simplify each side of the equation and see if they are equal.
Starting with the left side of the equation:
x/2 - x/(x-4)
First, we need to find a common denominator for the two fractions, which is 2(x-4):
(x(x-4))/(2(x-4)) - x/(x-4)
Expanding the numerator of the first fraction:
(x^2-4x)/(2(x-4)) - x/(x-4)
Combining the two fractions:
((x^2-4x) - 2x) / (2(x-4))
Simplifying:
(x^2-4x-2x)/(2(x-4))
(x^2-6x)/(2(x-4))
Now let's simplify the right side of the equation:
-4/(x-4)
Since there is no denominator to simplify, we can rewrite the expression:
-4/(x-4) = -4/(x-4)
Now, let's check if the left and right sides are equal:
(x^2-6x)/(2(x-4)) = -4/(x-4)
To determine if these expressions are equal, we can multiply both sides of the equation by (x-4) to get rid of the denominators:
(x^2-6x) = -4
Now let's rearrange the right side to get it in the same form as the left side:
-4 = x^2 - 6x
Now, we have a quadratic equation. To check further, we can simplify the equation by moving all terms to one side:
x^2 - 6x - 4 = 0
To check if this quadratic equation is true, we can factor it or use the quadratic formula:
Using the quadratic formula: x = (-b ± √(b^2-4ac))/(2a)
For the equation x^2-6x-4 = 0, a = 1, b = -6, and c = -4.
x = (-(-6) ± √((-6)^2-4(1)(-4))) / (2(1))
x = (6 ± √(36 + 16)) / 2
x = (6 ± √(52)) / 2
x = (6 ± √(4*13)) / 2
x = (6 ± 2 √(13)) / 2
Simplifying:
x = 3 ± √(13)
Therefore, the equation x/2 - x/(x-4) = -4/(x-4) = -4x^2/2 holds true if x = 3 ± √(13).