Solve 1 by x-3 + 2 by x-2 = 8 by x

1.	Solve 1 by x-3 + 2 by x-2 = 8 by x
Answer» We have,{tex}\\frac{1}{{x - 3}} + \\frac{2}{{x - 2}} = \\frac{8}{x}{/tex}{tex}\\Rightarrow \\frac{{1(x - 2) + 2(x - 3)}}{{(x - 3)(x - 2)}} = \\frac{8}{x}{/tex}{tex}\\Rightarrow \\frac{{x - 2 + 2x - 6}}{{(x - 3)(x - 2)}} = \\frac{8}{x}{/tex}{tex}\\Rightarrow \\frac{{3x - 8}}{{{x^2} - 2x - 3x + 6}} = \\frac{8}{x}{/tex}{tex}\\Rightarrow \\frac{{3x - 8}}{{{x^2} - 5x + 6}} = \\frac{8}{x}{/tex}Cross multiply,{tex}\\Rightarrow{/tex}\xa0{tex}x(3x-8)=8(x^2-5x+6){/tex}{tex}\\Rightarrow{/tex}\xa0{tex}3x^2-8x=8x^2-40x+48{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}8x^2-40x+48-3x^2+8x=0{/tex}{tex}\\Rightarrow{/tex}\xa0{tex}5x^2-32x+48=0{/tex}Factorise the equation,{tex}\\Rightarrow{/tex} 5x2 - 20x - 12x + 48 = 0{tex}\\Rightarrow{/tex} 5x(x - 4) - 12(x - 4) = 0{tex}\\Rightarrow{/tex} (5x - 12) (x - 4) = 0{tex}\\Rightarrow{/tex} (5x - 12) = 0 or (x - 4) = 0{tex} \\Rightarrow x = \\frac{{12}}{5}{/tex} or x = 4

Discussion