Answer:
x = - 12
Step-by-step explanation:
Given
[tex]\frac{x}{x+4}[/tex] + [tex]\frac{7}{x-2}[/tex] = 1
Multiply through by (x + 4)(x - 2) to clear the fractions
x(x - 2) + 7(x + 4) = (x + 4)(x - 2) ← expand using FOIL
x² - 2x + 7x + 28 = x² + 2x - 8
x² + 5x + 28 = x² + 2x - 8 ( subtract x² from both sides )
5x + 28 = 2x - 8 ( subtract 2x from both sides )
3x + 28 = - 8 ( subtract 28 from both sides )
3x = - 36 ( divide both sides by 3 )
x = - 12
