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 equation

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

Multiply both sides of the equation by $2$

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

Multiply the single term $2$ by each term of the polynomial $\left(x-1\right)$

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

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

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

Combine all terms into a single fraction with $3$ as common denominator

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

Multiply $-1$ times $3$

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

Subtract the values $-2$ and $-3$

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

Expand the fraction $\frac{-5+2x}{3}$ into $2$ simpler fractions with common denominator $3$

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

Divide $-5$ by $3$

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

Grouping terms

$\frac{4}{3}x=-\frac{5}{3}$

Eliminate the $\frac{4}{3}$ from the left side, multiplying both sides of the equation by the inverse of $\frac{4}{3}$

$x=-\frac{5}{4}$

Final Answer