simplify fully!
3x-2/x+4 = 18-4x/x^2-16 - 3x+2/4-x
show all of your steps pleasee !!
i need help asap
Do you mean you want to solve the equation?
(3x-2)/(x+4) = (18-4x)/(x^2-16) - (3x+2)/(4-x)
You need a common denominator. Since x^2-16 = (x-2)(x+2), then assuming x ≠ ±4,
(3x-2)(x-4) = (18-4x) + (3x+2)(x+4)
Now you can rearrange terms to get
-6(4x+3) = 0
so, x = -3/4
To simplify the expression fully, we will first find the common denominator for all the fractions in the equation. Then, we will combine like terms and simplify as much as possible. Let's break down the steps:
Step 1: Finding the common denominator
The denominators in the equation are (x + 4), (x^2 - 16), and (4 - x). To find the common denominator, we need to factor the second fraction's denominator, which is (x^2 - 16). It can be written as (x + 4)(x - 4). So, the common denominator is (x + 4)(x - 4).
Step 2: Simplifying the fractions
Now, let's rewrite the equation with the common denominator:
((3x - 2)/(x + 4)) = ((18 - 4x)/((x + 4)(x - 4))) - ((3x + 2)/(4 - x))
Step 3: Combine the numerators
((3x - 2)/(x + 4)) = ((18 - 4x) - (3x + 2))/(x + 4)(x - 4))
Simplifying the numerators:
(3x - 2)/(x + 4) = (18 - 4x - 3x - 2)/(x + 4)(x - 4)
Step 4: Combine like terms
(3x - 2)/(x + 4) = (18 - 7x - 2)/(x + 4)(x - 4)
Step 5: Distribute the common denominator
(x + 4)(x - 4) * (18 - 7x - 2) = (3x - 2)(x + 4)(x - 4)
Step 6: Simplify further if possible
(x + 4)(x - 4) * (16 - 7x) = (3x - 2)(x + 4)(x - 4)
The expression is now simplified.