👉 Try now NerdPal! Our new math app on iOS and Android
  1. calculators
  2. Rational Equations

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.

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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

Apply fraction cross-multiplication

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

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

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

Any expression multiplied by $1$ is equal to itself

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

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

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

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

$3x+3=2x+2\cdot -1$

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

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

Any expression multiplied by $1$ is equal to itself

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

Multiply $2$ times $-1$

$3x+3=2x-2$
5

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

$3x+3=2x-2$
6

Group the terms of the equation by moving the terms that have the variable $x$ to the left side, and those that do not have it to the right side

$3x-2x=-2-3$
7

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

$3x-2x=-5$
8

Combining like terms $3x$ and $-2x$

$x=-5$

Verify that the solutions obtained are valid in the initial equation

9

The valid solutions to the equation are the ones that, when replaced in the original equation, don't make any denominator equal to $0$, since division by zero is not allowed

$x=-5$

Final Answer

$x=-5$

Struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!