Solve the following equation - 1-x-1-1-x-1-x-3-1-x-4

1/x 1 1/x=1/x+3 1/x+4 ⇒ x (x 1)/(x 1)x=(x+4) (x+3)/(x+3)(x+4) =1/(x 1)x=1/(x+3)(x+4) =(x+3)(x+4)=x(x 1) ⇒ x^2+4x+3x+12=x^2 x ⇒ x^2+7x x^2+x= 12 8x= 12 ...

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Standard VIII

Mathematics

Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equation :

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

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Solution

$\frac{1}{x - 1} - \frac{1}{x} = \frac{1}{x + 3} - \frac{1}{x + 4} \Rightarrow \frac{x - (x - 1)}{(x - 1) x} = \frac{(x + 4) - (x + 3)}{(x + 3) (x + 4)} = \frac{1}{(x - 1) x} = \frac{1}{(x + 3) (x + 4)} = (x + 3) (x + 4) = x (x - 1) \Rightarrow x^{2} + 4 x + 3 x + 12 = x^{2} - x \Rightarrow x^{2} + 7 x - x^{2} + x = - 12 8 x = - 12 x = - \frac{12}{8} = - \frac{3}{2} = - 1 \frac{1}{2}$

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\frac{1}{x - 1} - \frac{1}{x} = \frac{1}{x + 3} - \frac{1}{x + 4}

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Solve the following equation : 1x−1−1x=1x+3−1x+4

1x−1−1x=1x+3−1x+4⇒ x−(x−1)(x−1)x=(x+4)−(x+3)(x+3)(x+4) =1(x−1)x=1(x+3)(x+4) =(x+3)(x+4)=x(x−1)⇒ x2+4x+3x+12=x2−x⇒ x2+7x−x2+x=−128x=−12x=−128=−32=−112

Solve the following equation :

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