👉 Try now NerdPal! Our new math app on iOS and Android

Solve the rational equation $xz=\frac{z^{-3}}{\left(1-z^{-1}\right)\left(1-\frac{1}{5}z^{-1}\right)}$

Step-by-step Solution

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

Final Answer

$x=\frac{5}{\left(5z-1\right)\left(z-1\right)z^{2}}$
Got another answer? Verify it here!

Step-by-step Solution

Specify the solving method

1

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$xz=\frac{1}{\left(1-z^{-1}\right)\left(1-\frac{1}{5}z^{-1}\right)z^{3}}$

Learn how to solve sum rule of differentiation problems step by step online.

$xz=\frac{1}{\left(1-z^{-1}\right)\left(1-\frac{1}{5}z^{-1}\right)z^{3}}$

Unlock unlimited step-by-step solutions and much more!

Create a free account and unlock a glimpse of this solution.

Learn how to solve sum rule of differentiation problems step by step online. Solve the rational equation xz=(z^(-3))/((1-z^(-1))(1-1/5z^(-1))). Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number. Divide both sides of the equality by z. When multiplying exponents with same base you can add the exponents: z\left(1-z^{-1}\right)\left(1-\frac{1}{5}z^{-1}\right)z^{3}. Applying the property of exponents, \displaystyle a^{-n}=\frac{1}{a^n}, where n is a number.

Final Answer

$x=\frac{5}{\left(5z-1\right)\left(z-1\right)z^{2}}$

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve for xSolve for zFind the discriminant

Give us your feedback!

Function Plot

Plotting: $xz+\frac{-z^{-3}}{\left(1-z^{-1}\right)\left(1-\frac{1}{5}z^{-1}\right)}$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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

How to improve your answer:

Main Topic: Sum Rule of Differentiation

The sum rule is a method to find the derivative of a function that is the sum of two or more functions.

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account