Rational equation
-5/x-3 - 3/x+3=2/x^2-9
how do I solve?
multiply everything by x^2-9, which gives you:
-5(x+3)-3(x-3)=2
Have fun!
9(x+3)-3(x+3)=2
9x+27+3-9=2
6x-36
6x=48
x=8
Is this right?
I apologize! I misread your equation. Multiply through by x^2 gives:
9x^2-8x-2=0. Use Quadratic Formula to get two solutions: (8+sqrt(136))/18 and (8-sqrt(136))/18. I checked, and both work!
To solve the rational equation (-5/(x-3)) - (3/(x+3)) = 2/(x^2-9), follow these steps:
Step 1: Simplify the equation:
First, let's simplify all the terms in the equation:
-5/(x-3) - 3/(x+3) = 2/(x^2-9)
To combine the fractions, we need to find a common denominator. In this case, the common denominator is (x-3)(x+3), which is the product of the denominators of both fractions.
Multiply each term by the necessary factors to get a common denominator:
(-5(x+3))/((x-3)(x+3)) - (3(x-3))/((x+3)(x-3)) = (2)/((x+3)(x-3))
Simplifying further, you would end up with:
(-5x - 15 - 3x + 9)/((x-3)(x+3)) = 2/((x+3)(x-3))
Combining like terms:
(-8x - 6)/((x-3)(x+3)) = 2/((x+3)(x-3))
Step 2: Eliminate the denominators:
To eliminate the denominators, you can multiply each side of the equation by (x-3)(x+3). This ensures that the denominators cancel out:
[(x-3)(x+3)] * [(-8x - 6)/((x-3)(x+3))] = [(x-3)(x+3)] * [2/((x+3)(x-3))]
Simplifying further:
(-8x - 6) = 2
Step 3: Solve for x:
Next, solve the resulting equation from step 2 for x:
-8x - 6 = 2
Add 6 to both sides:
-8x = 8
Divide both sides by -8:
x = -1
Therefore, the solution to the rational equation is x = -1.
Note: Before finalizing the solution, make sure to check if the obtained value satisfies any excluded values, in this case x=±3.