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 ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Solving Equations with Variables on Both Sides

Solve the fol...

Question

Solve the following equation :

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

Open in App

Solution

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

Suggest Corrections

Similar questions

Solve the following equation:

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

Q. Solve the following equation:

\sqrt{x + 3 - 4 \sqrt{x - 1}} + \sqrt{x + 8 - 6 \sqrt{x - 1}} = 1

Q. Solve the following:

\frac{x - 1}{x^{3 / 4} + x^{1 / 2}} \cdot \frac{x^{1 / 2} + x^{1 / 4}}{x^{1 / 2} + 1} \cdot x^{1 / 4} + 1

for

x = 16

Q. Solve the following quadratic equations by factorization:

\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}

Q. Solve the following system of inequality:

\frac{x}{3} - \frac{4}{3} ⩽ \frac{4}{x}, \frac{1}{x} > - 1, x^{2} + 3 x + 1 > 0

Join BYJU'S Learning Program

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 :

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