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Rational equations Calculator

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1

Solved example of rational equations

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

Inverting the inequation

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

Split the fraction $\frac{x+1}{2}$ in two fractions with common denominator $2$

$\frac{x}{2}+\frac{1}{2}=\frac{x-1}{3}$
4

Split the fraction $\frac{x-1}{3}$ in two fractions with common denominator $3$

$\frac{x}{2}+\frac{1}{2}=\frac{x}{3}-\frac{1}{3}$
5

We need to isolate the dependent variable $x$, we can do that by subtracting $\frac{1}{2}$ from both sides of the equation

$\frac{x}{2}=-\frac{5}{6}+\frac{x}{3}$
6

Multiply both sides of the equation by $2$

$x=2\left(-\frac{5}{6}+\frac{x}{3}\right)$
7

Grouping all terms to the left side of the equation

$x-2\left(-\frac{5}{6}+\frac{x}{3}\right)=0$
8

Solve the product $-2\left(-\frac{5}{6}+\frac{x}{3}\right)$

$x+\frac{5}{3}-2\left(\frac{x}{3}\right)=0$
9

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

$\frac{1}{3}x+\frac{5}{3}=0$
10

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

$\frac{1}{3}x=-\frac{5}{3}$
11

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

$x=-5$

Final Answer

$x=-5$

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