Question

Solve `5/(x - 2) -  3/(x + 6) = 4/x`

Answer 1

Given:

`5/(x - 2) - 3/(x + 6) = 4/x`

Step 1: Take LCM and eliminate denominators:

Multiply both sides by: x(x − 2)(x + 6)

Step 2: Simplify each term:

5(x)(x + 6) = 5x(x + 6)

3(x)(x − 2) = 3x(x − 2)

4(x − 2)(x + 6)

Step 3: Write the equation:

5x(x + 6) − 3x(x − 2) = 4 (x − 2)(x + 6)

Step 4: Expand both sides:

LHS: 5x² + 30x − 3x² + 6x = 2x² + 36x

RHS: 4(x² + 4x − 12) = 4x² + 16x − 48

Step 5: Final equation:

2x² + 36x = 4x + 16x − 48 ⇒ x² − 10x − 24 = 0

Step 6: Solve the quadratic:

x = 12 or x = −2