3 4 1
- + --- = - -
x x+2 x
sorry it posted stupid, its:
3/x + 4/x+2 = -1/x
3/x + 4/(x+2) = -1/x
multiply each term by x(x+2)
3(x+2) + 4x = -1(x+2)
expand and re-arrange, after that it is easy.
thank you
To find the value of x that satisfies the given equation, we can start by simplifying both sides of the equation.
On the left-hand side of the equation, we have:
3/x + 4/(x+2)
To simplify this expression, we need a common denominator. The common denominator for the two fractions is (x * (x+2)). We can then rewrite each fraction with this denominator:
(3 * (x+2))/(x * (x+2)) + (4 * x)/(x * (x+2))
Now, we can combine the fractions:
(3x + 6 + 4x)/(x * (x+2))
Simplifying further:
(7x + 6)/(x * (x+2))
On the right-hand side of the equation, we have:
- -x
To combine these fractions, we need to have a common denominator. In this case, the common denominator is (x * (x+2)), so we rewrite -x as (-x * (x+2))/(x * (x+2)):
(-x * (x+2))/(x * (x+2))
Now that we have a common denominator, we can combine the fractions:
(-x * (x+2) - 7x - 6)/(x * (x+2))
Now, the equation becomes:
(7x + 6)/(x * (x+2)) = (-x * (x+2) - 7x - 6)/(x * (x+2))
To solve for x, we can cross-multiply:
(7x + 6) * (x * (x+2)) = (-x * (x+2) - 7x - 6)
Expanding both sides of the equation:
7x * (x * (x+2)) + 6 * (x * (x+2)) = -x * (x+2) - 7x - 6
Simplifying further:
7x^3 + 14x^2 + 6x^2 + 12x = -x^2 - 2x - 7x - 6
Combining like terms:
7x^3 + 20x^2 + 12x = -x^2 - 9x - 6
Rearranging the equation to bring all terms to one side:
7x^3 + 20x^2 + 12x + x^2 + 9x + 6 = 0
Now, we have a cubic equation. To find its roots, we can use numerical or symbolic methods, such as factoring, synthetic division, or applying the cubic formula.
After solving the cubic equation, we will obtain the value(s) of x that satisfy the original equation.