Rational equations Calculator

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Example

Solved Problems

Difficult Problems

Solved example of rational equations

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

Apply fraction cross-multiplication

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

Solve the product $2\left(x-1\right)$

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

Solve the product $3\left(x+1\right)$

$2x-2=3x+3$

We need to isolate the dependent variable $x$, we can do that by subtracting $-2$ from both sides of the equation

$2x=5+3x$

Divide both sides of the equation by $2$

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

Split the fraction $\frac{5+3x}{2}$ in two fractions with common denominator $2$

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

Grouping terms

$-\frac{1}{2}x=\frac{5}{2}$

Eliminate the $-\frac{1}{2}$ from the left, multiplying both sides of the equation by $$

$x=-5$

Final Answer