i have this question and i kinda know how to do it but i'm not entirelly sure.

here's the problem

x-5/4 = x+5/x+2

if you can help great and thank you

Please use parentheses to rewrite your problem. For example, x-(5/4) = x+(5/x) + 2 or whatever; otherwise, we can't tall what is in the numerator and whatr is in the denominator.

x-5 x+5

___ = ___
4 x+2

First you want to cross multiply
(x-5)(x+2) = 4(x+5)
Then use FOIL on the left hand side, and distribute the 4 on the right hand side

to get X(squared)-3x -10 on the left
= 4x+20 on the right

subtract the 4x+20 on the right and left side

you get x(squared) -7x -30 =0

now find the roots of this equation
(x-10)(x+3)=0
x=10 and x=-3

Those are the solutions for x

Of course, I can help you with the problem. Let's work through it step by step.

The given equation is:

(x - 5) / 4 = (x + 5) / (x + 2)

To solve this equation, we need to get rid of the fractions. We can do this by multiplying both sides of the equation by the least common denominator (LCD) of 4 and (x + 2), which is 4(x + 2). By doing this, we will eliminate the denominators.

4(x + 2) * [(x - 5) / 4] = 4(x + 2) * [(x + 5) / (x + 2)]

Now, simplify the equation:

(x + 2) * (x - 5) = 4(x + 5)

Expand the terms:

x^2 - 3x - 10 = 4x + 20

Rearrange the equation by bringing all the terms to one side:

x^2 - 3x - 10 - 4x - 20 = 0

Combine like terms:

x^2 - 7x - 30 = 0

Now, we have a quadratic equation. To solve it, you can either factorize it if possible or use the quadratic formula.

In this case, the quadratic equation cannot be easily factored. So, let's use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / 2a

For our equation, the coefficients are a = 1, b = -7, and c = -30. Plugging these values into the formula:

x = (-(-7) ± √((-7)^2 - 4 * 1 * -30)) / (2 * 1)

Simplifying:

x = (7 ± √(49 + 120)) / 2

x = (7 ± √(169)) / 2

x = (7 ± 13) / 2

Now, we have two possible solutions:

1. x = (7 + 13) / 2 = 20 / 2 = 10
2. x = (7 - 13) / 2 = -6 / 2 = -3

Therefore, the possible values for x that satisfy the original equation are x = 10 and x = -3. To confirm these solutions, substitute them back into the original equation and check if both sides are equal for each value of x.