QuestionSolve the equation: $\frac{4}{x-4}=\frac{-4}{x+3}+\frac{12}{(x-4)(x+3)}$

Studdy Solution

STEP 1

Assumptions1. The given equation is $\frac{4}{x-4}=\frac{-4}{x+3}+\frac{12}{(x-4)(x+3)}$ . We are asked to find the value of x that satisfies this equation.

STEP 2

To simplify the equation, we will multiply the entire equation by the common denominator $(x-4)(x+)$ .
$4(x+) = -4(x-4) +12$

STEP 3

Now, we will simplify the equation by distributing the numbers inside the parentheses.
$x +12 = -x +16 +12$

STEP 4

Combine like terms on each side of the equation.
$4x +12 = -4x +28$

STEP 5

To isolate the variable x, we will add4x to both sides of the equation.
$4x +4x +12 = -4x +4x +28$

STEP 6

implify the equation.
$8x +12 =28$

STEP 7

Next, we will subtract12 from both sides of the equation to isolate the variable term.
$x +12 -12 =28 -12$

STEP 8

implify the equation.
$8x =16$

STEP 9

Finally, we will divide both sides of the equation by8 to solve for x.
$x = \frac{16}{8}$

STEP 10

implify to get the solution.
$x =2$ The solution to the equation is $x =2$ .

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