Solve: (x+5/x)+(6/x-4)=(-7/x^2-4x)

I multiplied the entire function by x and x-4 and after doing that I got down to the quadratic equation
x^2+7x-13=0

I did the quadratic and got

x=1.525 and -8.525

I feel like I made a mistake because when I plug in both of those answers for x separately, it never works out. Not sure if I made an error in calculating or in plugging in, or if there is no solution.

Thanks.

your answer is wrong.... redo the problem and move 1.5 and make it 5.125

I'm not quite sure what you mean. Can you please elaborate

Not sure you should go by me, because I took it down wrong the first time, but I got:

x + 11/x - 4 + 7/x^2 + 4x = 0

Gathering and multiplying by x^2:

5x^3 - 4x^2 + 11x + 7 = 0

Does this makes sense to you in the context of your course?

To solve the given equation:

1. Start by multiplying every term in the equation by x(x - 4) to clear the denominators.

So, we have:

x(x - 4) * (x + 5)/x + x(x - 4) * 6/(x - 4) = x(x - 4) * -7/(x^2 - 4x)

Simplifying this expression:

(x + 5)(x - 4) + 6x = -7

2. Expand and simplify:

(x^2 + x - 20) + 6x = -7

Combine like terms:

x^2 + 7x - 20 + 6x = -7

3. Continue simplifying:

x^2 + 13x - 20 + 7 = 0

x^2 + 13x - 13 = 0

4. Now, you mentioned that you got the quadratic equation x^2 + 7x - 13 = 0, but this is where the mistake is.

To solve the quadratic equation x^2 + 13x - 13 = 0, you can factorize or use the quadratic formula.

Using the quadratic formula, where a = 1, b = 13, and c = -13:

x = (-b ± √(b^2 - 4ac)) / (2a)

x = (-13 ± √(13^2 - 4(1)(-13))) / (2(1))

x = (-13 ± √(169 + 52)) / 2

x = (-13 ± √221) / 2

The solutions of the quadratic equation are:

x = (-13 + √221) / 2 and x = (-13 - √221) / 2

So, the correct solutions to the original equation are:

x = (-13 + √221) / 2 and x = (-13 - √221) / 2

It's important to double-check your calculations to ensure there are no errors in the final solutions.