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

Simplify the expression $\frac{s}{s^2+s+20}$

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

Step-by-step Solution

Specify the solving method

Final Answer

Sorry, we couldn't solve this problem right now. Please check back later or try another solving method.

Derivative

$\frac{d}{ds}\left(\frac{s}{s^2+s+20}\right)=\frac{s^2+s+20+\left(-2s-1\right)s}{\left(s^2+s+20\right)^2}$ See full solution

Integral

$\int\frac{s}{s^2+s+20}ds=-\frac{1}{\log^{3}\left(10\right)}\ln\left(\frac{\sqrt{\frac{79}{4}}}{\sqrt{\frac{79}{4}+\left(s+\frac{1}{2}\right)^2}}\right)-\frac{9}{80}\arctan\left(\frac{s+\frac{1}{2}}{\sqrt{\frac{79}{4}}}\right)+C_0$ See full solution

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

SimplifyWrite in simplest formFactorFactor by completing the squareFind the integralFind the derivativeFind s/(s^2+s) using the definitionSolve by quadratic formula (general formula)Find the rootsFind break even pointsFind the discriminant

Give us your feedback!

Main Topic: Simplification of algebraic fractions

Simplification or reduction of algebraic fractions is the action of dividing the numerator and denominator of a fraction by a common factor in order to obtain another much simpler equivalent fraction. We can say that a fraction is reduced to its simplest when there is no common factor between the numerator and the denominator.

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete 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