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.