# Rational equations Calculator

## Get detailed solutions to your math problems with our Rational equations step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

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### Difficult Problems

1

Solved example of rational equations

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

Inverting the equation

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

Multiply both sides of the equation by $2$

$x+1=\frac{2\left(x-1\right)}{3}$
4

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

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

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

$x=\frac{2x-2}{3}-1$
6

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

$x=\frac{2x-2-1\cdot 3}{3}$
7

Multiply $-1$ times $3$

$x=\frac{2x-2-3}{3}$
8

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

$x=\frac{-5+2x}{3}$
9

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

$x=\frac{-5}{3}+\frac{2x}{3}$
10

Divide $-5$ by $3$

$x=-\frac{5}{3}+\frac{2x}{3}$
11

Grouping terms

$\frac{4}{3}x=-\frac{5}{3}$
12

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

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

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