# Math Assignment Help With Inverse Transforms Of Rational Functions

## 4.8 Inverse Transforms of Rational Functions

Let *F*(s) be a rational function of s. Inverse Laplace transform of *F*(s).

**Example: **

**i)**

**If denominator of a function has distinct real roots:**

F(s) = (s + 1) (s + 3) find *f*(t)

s (s + 2) (s + 8)

**Solution:**

F(s) = 3 + 1 + 35

16s 1(s + 2) 48(s + 8)

Thus,

*F*(t) = 3 + 1 e^{-2t} 35 e^{-8t}

16 12 48

**ii)**

**Denominator of a function has distinct complex roots:**

If F(s) = 4s + 3 find *f*(t)

s^{2} + 2s + 5

<**Solution**: F(s) = 4 s + 1 - 1 2

(s + 1)^{2} + 2^{2} 2 (s + 1)^{2} + 2^{2}

Thus,

*F*(t) = 4e^{-t} cos(2t) – 1 e^{-1} sin(2t)

**iii)**

**Denominator of a function has repeated real roots:**

*F(s)*** = **3s + 4 find *f*(t)

(s + 1) (s^{2} + 4s+ 4)

### Email Based Assignment Help in Inverse Transforms Of Rational Functions

**To Schedule an Inverse Transforms Of Rational Functions tutoring session
To submit Inverse Transforms Of Rational Functions assignment click here.**

### Following are some of the topics in Rational Function in which we provide help:

Assignment Help Features

- 24 x 7 Availability.
- Plagiarism Free.
- Trained and Certified Experts.
- Deadline Guaranteed.
- Privacy Guaranteed.
- Assignment Help Reward
- Online help for all project.
- Service for everyone
- Online Tutoring
- Free download.
- Whitepaper.

Assignment Help Services

- Assignment Help
- Homework Help
- Writing Help
- Academic Writing Assistance
- Editing Services
- Plagiarism Checker Online
- Proofreading
- Research Writing Help

Calculator