2/x+3=3/x-5
same type as the one I answered below
OK. THANK YOU.
1x1
To solve the equation 2/x + 3 = 3/x - 5, you need to follow these steps.
Step 1: Get rid of the denominators
- Multiply every term in the equation by the least common multiple (LCM) of the denominators. In this case, the LCM of x and x-5 is (x)(x-5). So, we multiply every term by x(x-5):
x(x-5) * (2/x) + x(x-5) * 3 = x(x-5) * (3/x) - 5 * x(x-5)
After multiplying, the equation becomes:
2(x-5) + 3x(x-5) = 3(x)(x-5) - 5(x)(x-5)
Step 2: Simplify the equation
- Expand the expressions on both sides of the equation, combining like terms:
2x - 10 + 3x^2 - 15x = 3x^2 - 15x - 5x^2 + 25x
Simplifying further:
-13x - 10 = -2x^2 + 10x
Step 3: Move all the terms to one side
- Rearrange the equation so that all terms are on one side and zero is on the other side:
2x^2 + 23x - 10 = 0
Step 4: Solve the quadratic equation
- You can solve the quadratic equation in different ways, for example, by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring, if possible:
(2x - 1)(x + 10) = 0
Setting each factor equal to zero:
2x - 1 = 0 or x + 10 = 0
Solving for x in each equation:
2x = 1 or x = -10
x = 1/2 or x = -10
So, the solutions to the original equation 2/x + 3 = 3/x - 5 are x = 1/2 and x = -10.