Solve the rational equation $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$.
Given: Equation $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$.
To do: To solve $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$.
Solution:
Given equation: $\frac{2}{(x-3)} + \frac{1}{x} = \frac{(x-1)}{(x-3)}$
$\Rightarrow \frac{2x+x-3}{x( x-3)}=\frac{(x-1)}{(x-3)}$
$\Rightarrow \frac{3x-3}{x}=x-1$
$\Rightarrow \frac{3( x-1)}{x}=( x-1)$
$\Rightarrow \frac{1}{x}=1$
$\Rightarrow x=1$
Thus, $x=1$.
Related Articles
- Solve the following quadratic equation by factorization: $\frac{1}{(x-1)(x-2)}+\frac{1}{(x-2)(x-3)}+\frac{1}{(x-3)(x-4)}=\frac{1}{6}$
- Solve for $x$:$\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3}, x≠2, 4$
- Solve for x:$\frac{1}{( x-1)( x-2)} +\frac{1}{( x-2)( x-3)} =\frac{2}{3} \ ,\ x\neq 1,2,3$
- Solve the following quadratic equation by factorization: $\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3}, x≠2, 4$
- Solve for $x$:$\frac{1}{x}+\frac{2}{2x-3}=\frac{1}{x-2}, x≠0, \frac{3}{2}, 2$
- Solve: \( \frac{x+5}{2}=1+\frac{2 x-1}{3} \).
- Solve the following:If $x^{2}+\frac{1}{x^{2}}=3,$ find a) $ x-\frac{1}{x}$b) $x+\frac{1}{x} $
- If \( x+\frac{1}{x}=3 \), calculate \( x^{2}+\frac{1}{x^{2}}, x^{3}+\frac{1}{x^{3}} \) and \( x^{4}+\frac{1}{x^{4}} \).
- Solve \( \frac{2 x+1}{3 x-2}=1\frac{1}{4} \).
- Solve the following linear equation.\( \frac{x}{2}-\frac{1}{5}=\frac{x}{3}+\frac{1}{4} \).
- Solve the following quadratic equation by factorization: $\frac{x+1}{x-1}+\frac{x-2}{x+2}=4-\frac{2x+3}{x-2}, x ≠ 1, -2, 2$
- Solve the following quadratic equation by factorization: $\frac{3}{x+1}-\frac{1}{2}=\frac{2}{3x-1}, x ≠-1, \frac{1}{3}$
- Solve the following quadratic equation by factorization: $\frac{1}{x\ -\ 3}\ +\ \frac{2}{x\ -\ 2}\ =\ \frac{8}{x};\ x\ ≠\ 0,\ 2,\ 3$
- Solve for $x$:$\frac{1}{x-3}-\frac{1}{x+5}=\frac{1}{6}, x≠3, -5$
- Solve for $x$:\( 3 x-\frac{x-2}{3}=4-\frac{x-1}{4} \)
Kickstart Your Career
Get certified by completing the course
Get Started