I am completely lost trying to solve this problem. I could really use some help and explanation.

x/x+1 + 5/x = 1/x^2+x

also how do you write

(x-5)(x-5) would it be x^2-5

You need parenthesis.

I'll assume your problem is,
x/(x+1) + 5/x = 1/(x^2 + x)
x/(x+1) + 5/x = 1/(x(x + 1))
Multiply both sides by x(x + 1)
x^2 + 5(x + 1) = 1
x^2 + 5x + 5 = 1
x^2 + 5x + 4 = 0
(x + 1)(x + 4) = 0

x = -1 or x = -4

Make sure you check both answers in the original equation. I have NOT checked.

I have been trying to figure this problem out and I am completely lost.

Could someone help guide me through it?

(3x^4-0x^3-8x^2 -3x-3) / (x^2-3)

Sure! I'll be happy to help you with both the problem and explaining how to solve it. Let's start with the problem:

To solve the equation:

x/(x + 1) + 5/x = 1/(x^2 + x)

We need to find the value(s) of x that satisfy this equation. Here's how we can proceed:

Step 1: Eliminate the denominators by multiplying both sides of the equation by the least common multiple (LCM) of the denominators. In this case, the LCM of (x + 1), x, and (x^2 + x) is x(x + 1)(x + 1):

x(x + 1)(x + 1) * [x/(x + 1) + 5/x] = x(x + 1)(x + 1) * [1/(x^2 + x)]

Simplifying this equation gives us:

x(x + 1)(x + 1) * (x/(x + 1) + 5/x) = x(x + 1)(x + 1) * (1/(x^2 + x))

Step 2: Distribute and simplify the equation:

x(x + 1)(x + 1) * (x/(x + 1)) + x(x + 1)(x + 1) * (5/x) = x(x + 1)(x + 1) * (1/(x^2 + x))

Canceling out common factors:

x(x + 1) + 5(x + 1) = 1

Expanding:

x^2 + x + 5x + 5 = 1

Combining like terms:

x^2 + 6x + 5 = 1

Rewriting the equation:

x^2 + 6x + 5 - 1 = 0

Simplifying the left side:

x^2 + 6x + 4 = 0

Step 3: Solve the quadratic equation. We can do this by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 4)(x + 1) = 0

Setting each factor equal to zero and solving for x:

x + 4 = 0 or x + 1 = 0

x = -4 or x = -1

Therefore, the solutions to the equation are x = -4 and x = -1.

Now, let's move on to your second question about how to write (x - 5)(x - 5):

When we multiply (x - 5) by itself, we use a method called FOIL:

F - First terms: x * x = x^2
O - Outer terms: x * (-5) = -5x
I - Inner terms: (-5) * x = -5x
L - Last terms: (-5) * (-5) = 25

Putting it all together, we have:

(x - 5)(x - 5) = x^2 - 5x - 5x + 25

Simplifying, the expression becomes:

(x - 5)(x - 5) = x^2 - 10x + 25

So, the correct expression for (x - 5)(x - 5) is x^2 - 10x + 25.

I hope this explanation helps! Let me know if you have any further questions.