Question

Solve for x : 1/(x - 1) - 1/x = 1/(x + 3) - 1/(x + 4)

Correct answer Options:

1) 1.5
2) -1.5
3) 2

Answer 1

$\large\underline{\sf{Given- }}$

$\bf :\longmapsto\:\dfrac{1}{x - 1} - \dfrac{1}{x} = \dfrac{1}{x + 3} - \dfrac{1}{x + 4}$

$\large\underline{\sf{To\:Find - }}$

$\: \: \: \: \: \: \: \: \bull \sf \: The \: value \: of \: x$

$\large\underline{\sf{Solution-}}$

$\rm :\longmapsto\:\dfrac{1}{x - 1} - \dfrac{1}{x} = \dfrac{1}{x + 3} - \dfrac{1}{x + 4}$

• On taking LCM of both the sides, we get

$\rm :\longmapsto\:\dfrac{x - (x - 1)}{x(x - 1)} = \dfrac{x + 4 - (x + 3)}{(x + 3)(x + 4)}$

$\rm :\longmapsto\:\dfrac{ \cancel x - \cancel x + 1}{x(x - 1)} = \dfrac{\cancel{x} + 4 - \cancel{x} - 3}{(x + 3)(x + 4)}$

$\rm :\longmapsto\:\dfrac{ 1 }{x(x - 1)} = \dfrac{1}{(x + 3)(x + 4)}$

$\rm :\longmapsto\:(x + 3)(x + 4) = x(x - 1)$

$\rm :\longmapsto\: \cancel{x}^{2} + 3x + 4x + 12 = \cancel {x}^{2} - x$

$\rm :\longmapsto\:8x = - 12$

$\bf\implies \boxed{ \bf{ \:x = - \dfrac{3}{2} = - 1.5}}$

$\boxed{ \bf{Hence, \: Option \: (2) \: is \: correct}}$

Additional Information :-

We can use the following steps to find a solution using transposition method:

• Step 1) Identify the variables and constants in the given simple equation.

• Step 2) Simplify the equation in and .

• Step 3) Transpose the term on the other side to solve the equation further simplest.

• Step 4) Simplify the equation using arithmetic operation as required that is mentioned in rule 1 or rule 2 of linear equations.

• Step 5) Then the result will be the solution for the given linear equation.