x-1/x+3=x+2/x-4
PLEASE tell us the School Subject so the right volunteer teacher will see it.
Sra
I think your question is not the way you typed it, but rather ....
(x-1)/(x+3) = (x+2)/(x-4) , if so, then
(x-1)(x-4) = (x+2)(x+3)
x^2 - 5x + 4 = x^2 + 5x + 6
-10x = 2
x = -1/5
To solve the given equation:
x - 1 / x + 3 = x + 2 / x - 4
Step 1: Clear the fractions
To get rid of the fractions, we need to find a common denominator for both sides of the equation. In this case, the common denominator is (x + 3)(x - 4), since it contains both (x + 3) and (x - 4).
Multiply both sides of the equation by (x + 3)(x - 4):
(x - 1) * (x - 4) = (x + 2) * (x + 3)
This will eliminate the denominators and leave us with a quadratic equation.
Step 2: Expand and simplify
Now, let's expand and simplify both sides of the equation:
(x^2 - 4x - x + 4) = (x^2 + 3x + 2x + 6)
Simplifying further:
(x^2 - 5x + 4) = (x^2 + 5x + 6)
Step 3: Combine like terms
Next, let's expand and organize the equation by combining like terms on both sides:
x^2 - 5x + 4 = x^2 + 5x + 6
Step 4: Move all terms to one side of the equation
To solve for x, we want to have all the terms on one side of the equation. Let's subtract x^2 from both sides:
-5x + 4 = 5x + 6
Step 5: Move variables to one side and constants to the other
Now, let's move the variables (5x) to one side and the constants (4 and 6) to the other side.
Subtract 5x from both sides:
4 = 10x + 6
Subtract 6 from both sides:
4 - 6 = 10x
Simplifying:
-2 = 10x
Step 6: Solve for x
To solve for x, divide both sides of the equation by 10:
-2 / 10 = x
Simplifying the division:
-1/5 = x
Therefore, the value of x that solves the equation is x = -1/5.