Solve the following equation - 1-x-1-2-x-2-3-x-3

1/x 1+2/x 2=3/x 3 =1(x 2)+2(x 1)/(x 1)(x 2)=3/x 3 ⇒ x 2+2x 2/x^2 2x x+2=3/x 3 ⇒ 3x 4/x^2 3x+2=3/x 3 ⇒ (x 3)(3x 4)=3(x^2 3x+2) ⇒ 3x^2 4x 9x+12=3x^2 9x+6 ⇒ 3x^2 ...

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Byju's Answer

Standard VIII

Mathematics

Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equation :

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

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Solution

$\frac{1}{x - 1} + \frac{2}{x - 2} = \frac{3}{x - 3} = \frac{1 (x - 2) + 2 (x - 1)}{(x - 1) (x - 2)} = \frac{3}{x - 3} \Rightarrow \frac{x - 2 + 2 x - 2}{x^{2} - 2 x - x + 2} = \frac{3}{x - 3} \Rightarrow \frac{3 x - 4}{x^{2} - 3 x + 2} = \frac{3}{x - 3} \Rightarrow (x - 3) (3 x - 4) = 3 (x^{2} - 3 x + 2) \Rightarrow 3 x^{2} - 4 x - 9 x + 12 = 3 x^{2} - 9 x + 6 \Rightarrow 3 x^{2} - 13 x - 3 x^{2} + 9 x = 6 - 12 \Rightarrow - 4 x = - 6 x = \frac{- 6}{- 4} = \frac{3}{2} = 1 \frac{1}{2}$

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Solve the following equation : 1x−1+2x−2=3x−3

1x−1+2x−2=3x−3=1(x−2)+2(x−1)(x−1)(x−2)=3x−3⇒ x−2+2x−2x2−2x−x+2=3x−3⇒ 3x−4x2−3x+2=3x−3⇒ (x−3)(3x−4)=3(x2−3x+2)⇒ 3x2−4x−9x+12=3x2−9x+6⇒ 3x2−13x−3x2+9x=6−12⇒ −4x=−6x=−6−4=32=112

Solve the following equation :

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