Using change of variable to solve 2/3x^2-x-2 +5/3x^2-x-1=7/3x^2-x-3
let u = 3x^2-x-2. Then you have
2/u + 5/(u+1) = 7/(u-1)
That gives you
u = -1/6
Now all you have to do is solve
3x^2-x-2 = -1/6
Combine terms.
The x^2 terms cancel out.
-2x-3 = -x-3
-x = 0
Do you have typos?
To solve the equation 2/3x^2 - x - 2 + 5/3x^2 - x - 1 = 7/3x^2 - x - 3, we can simplify it by combining like terms:
First, let's rearrange the equation in ascending order of x^2, x, and constant terms:
(2/3x^2 + 5/3x^2 - 7/3x^2) + (-x - x + x) + (-2 - 1 + 3) = 0
Combining the like terms, we get:
(2/3 + 5/3 - 7/3)x^2 + (-1 - 1 + 1)x + (-2 - 1 + 3) = 0
Simplifying further:
(0)x^2 + (-1)x + (0) = 0
Now, we have a simpler equation of -x = 0.
To solve for x, we can use the change of variable method:
Let's introduce a new variable, say u, to simplify the equation. We make the substitution that u = -x.
Now, we need to express the original equation in terms of u instead of x.
Let's rewrite the equation using the new variable:
-u = 0
Since -u = 0 has a simpler form and we know that u = -x, we can conclude that -x = 0 or x = 0.
Therefore, the solution to the original equation is x = 0.