6/x + 6/x-5 = 1
I got to x^2 -17x +5 = 0
But I have no idea if that is right?
How do I find the answer?
Thanks
6/x 6/x-5 =1
multiply both sides by x
x(6/x +6/x-5)= (1) x
The denominator x will cancel giving:
6 + 6
--- = x
-5
Now -5 into 6 = -1.2
so 6 -1.2= x
x= 4.8
To solve the equation 6/x + 6/(x-5) = 1, you can follow these steps:
Step 1: Multiply both sides of the equation by the common denominator, which is x(x-5). This will eliminate the denominators in the equation.
x(x-5)(6/x) + x(x-5)(6/(x-5)) = x(x-5)(1)
Simplifying this, we have:
6(x-5) + 6x = x(x-5)
Step 2: Expand and simplify the equation by distributing and combining like terms.
6x - 30 + 6x = x^2 - 5x
12x - 30 = x^2 - 5x
Rearrange the equation to bring all terms to one side:
x^2 - 17x + 30 = 0
Step 3: Now, you need to solve this quadratic equation. To do so, you can use factoring, completing the square, or the quadratic formula. Since the equation you got, x^2 - 17x + 30 = 0, can be factored, let's factor it.
(x - 2)(x - 15) = 0
This means that either (x - 2) = 0 or (x - 15) = 0.
Solving each equation individually, we have:
For (x - 2) = 0, adding 2 to both sides gives:
x = 2
For (x - 15) = 0, adding 15 to both sides gives:
x = 15
So, the solutions to the equation 6/x + 6/(x-5) = 1 are x = 2 and x = 15.
To solve the equation 6/x + 6/(x-5) = 1, you can follow these steps:
1. Multiply both sides of the equation by x(x-5) to eliminate the denominators:
x(x-5) * (6/x) + x(x-5) * (6/(x-5)) = x(x-5) * 1
2. Simplify the equation:
6(x-5) + 6x = x(x-5)
3. Distribute:
6x - 30 + 6x = x^2 - 5x
4. Combine like terms on the left side:
12x - 30 = x^2 - 5x
5. Move all terms to one side to set the equation to zero:
x^2 - 5x - 12x + 30 = 0
x^2 - 17x + 30 = 0
Now you need to factor this quadratic equation or use the quadratic formula to find the values of x.
6. Factor the quadratic equation:
(x - 2)(x - 15) = 0
7. Set each factor to zero:
x - 2 = 0 or x - 15 = 0
8. Solve for x separately:
x = 2 or x = 15
Therefore, the solutions to the equation 6/x + 6/(x-5) = 1 are x = 2 or x = 15.