Rational equations Calculator

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Example

Solved Problems

Difficult Problems

Solved example of rational equations

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

Inverting the inequation

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

Multiply both sides of the equation by $2$

$x+1=2\left(\frac{x-1}{3}\right)$

Simplify the fraction $2\left(\frac{x-1}{3}\right)$

$x+1=\frac{2}{3}\left(x-1\right)$

Solve the product $\frac{2}{3}\left(x-1\right)$

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

We need to isolate the dependent variable $x$, we can do that by subtracting $1$ from both sides of the equation

$x=-\frac{5}{3}+\frac{2}{3}x$

Rearrange the equation

$-\frac{5}{3}+\frac{2}{3}x=x$

We need to isolate the dependent variable $x$, we can do that by subtracting $-\frac{5}{3}$ from both sides of the equation

$\frac{2}{3}x=x+\frac{5}{3}$

Grouping terms

$-\frac{1}{3}x=\frac{5}{3}$

Eliminate the $-\frac{1}{3}$ from the left, multiplying both sides of the equation by $$

$x=-5$

Final Answer