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Solve the rational equation $\frac{x}{x-1}+\frac{4}{x\left(x-1\right)}=\frac{5}{x-1}$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=4$
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Step-by-step Solution

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The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors

$L.C.M.=\left(x-1\right)x$

Learn how to solve rational equations problems step by step online.

$L.C.M.=\left(x-1\right)x$

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Learn how to solve rational equations problems step by step online. Solve the rational equation x/(x-1)+4/(x(x-1))=5/(x-1). The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors. Obtained the least common multiple (LCM), we place it as the denominator of each fraction, and in the numerator of each fraction we add the factors that we need to complete. Combine and simplify all terms in the same fraction with common denominator \left(x-1\right)x. Multiply the whole equality by x-1.

Final answer to the problem

$x=4$

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Function Plot

Plotting: $\frac{x}{x-1}+\frac{4}{x\left(x-1\right)}+\frac{-5}{x-1}$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

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Similar Problems Solved

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

$3+\frac{1}{x}=\frac{10}{x^2}$

$\frac{2x+6}{3x}=x-8$

$\frac{x}{x-1}+\frac{4}{x\left(x-1\right)}=\frac{5}{x-1}$

$5\left(a+2\right)=\frac{40}{a}+\frac{2a}{3}$

$c-2=\frac{18}{c}+7$

$60=arccos\left(\frac{10}{x}\right)$

Main Topic: Rational Equations

Rational or fractional equations are those equations that contain algebraic fractions, and where the variable or unknown appears in the denominator of at least one of those fractions.

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