Answer:
x = [tex]\frac{9}{4}[/tex] or 2.5
Step-by-step explanation:
[tex]\frac{4}{x-3} + \frac{2}{x-2} = \frac{6}{x}[/tex]
Finding L.C.M. of (x - 3) and (x - 2)
[tex]\frac{4(x-2) + 2(x-3) }{(x-3)(x-2)} = \frac{6}{x}[/tex]
[tex]\frac{(4x-8) + (2x-6)}{x^{2} - 3x-2x+6}=\frac{6}{x}[/tex]
[tex]\frac{4x-8 +2x-6}{x^{2} -5x +6} = \frac{6}{x}[/tex]
[tex]\frac{6x-14}{x^{2} -5x+6}= \frac{6}{x}[/tex]
Cross multiplying:
x (6x - 14) = 6 (x² - 5x +6)
6x² - 14x = 6x² - 30x + 36
Cancelling 6x² from both the sides:
- 14x = - 30x + 36
30x - 14x = 36
16x = 36
x = [tex]\frac{36}{16}[/tex]
∴ x = [tex]\frac{9}{4}[/tex] or 2.5
