Solve each of the following quadratic equations- 1-x-2-2-x-1-6-x-x - 0-1-2

1/x 2+2/x 1=6/x 1(x 1)+2(x 2)/x^2 x 2x+2=6/x x 1+2x 4/x^2 3x+2=6/x 3x 5/x^2 3x+2=6/x 3x^2 5x = 6x^2 18x+12 6x^2 3x^2 18x+5x+12=0 3x^2 13x+12=0 3x^2 9x 4x+12=0 3 ...

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Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

Solve each of...

Question

Solve each of the following quadratic equations:
$\frac{1}{x - 2} + \frac{2}{x - 1} = \frac{6}{x}, x \neq 0, 1, 2$

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Solution

$\frac{1}{x - 2} + \frac{2}{x - 1} = \frac{6}{x}$

$\frac{1 (x - 1) + 2 (x - 2)}{x^{2} - x - 2 x + 2} = \frac{6}{x}$

$\frac{x - 1 + 2 x - 4}{x^{2} - 3 x + 2} = \frac{6}{x}$

$\frac{3 x - 5}{x^{2} - 3 x + 2} = \frac{6}{x}$

$3 x^{2} - 5 x = 6 x^{2} - 18 x + 12$

$6 x^{2} - 3 x^{2} - 18 x + 5 x + 12 = 0$

$3 x^{2} - 13 x + 12 = 0$

$3 x^{2} - 9 x - 4 x + 12 = 0$

$3 x (x - 3) - 4 (x - 3) = 0$

$(3 x - 4) (x - 3) = 0$

$x = 3 o r \frac{4}{3}$

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Solve each of the following quadratic equations: 1x−2+2x−1=6x,x≠0,1,2

1x−2+2x−1=6x 1(x−1)+2(x−2)x2−x−2x+2=6x x−1+2x−4x2−3x+2=6x 3x−5x2−3x+2=6x 3x2−5x=6x2−18x+12 6x2−3x2−18x+5x+12=0 3x2−13x+12=0 3x2−9x−4x+12=0 3x(x−3)−4(x−3)=0 (3x−4)(x−3)=0 x=3 or 43

Solve each of the following quadratic equations:
$\frac{1}{x - 2} + \frac{2}{x - 1} = \frac{6}{x}, x \neq 0, 1, 2$