Question

Obtain an expression that looks like this: 25+ 4 А B. X(S) = + s(s +6) S +6 S

Answer 1

Answer:

$A = \frac{2}{3}$

$B = \frac{4}{3}$

Step-by-step explanation:

Given

$X(s) = \frac{2s + 4}{s(s +6)}= \frac{A}{s} + \frac{B}{s + 6}$

Required

Find A and B

The expression can be rewritten as

$\frac{2s + 4}{s(s +6)}= \frac{A}{s} + \frac{B}{s + 6}$

Take LCM of the right hand side

$\frac{2s + 4}{s(s +6)}= \frac{A(s + 6 )+ Bs}{s(s +6)}$

Cancel out the denominators

$2s + 4 = A(s + 6) + Bs$

Open Bracket

$2s + 4 = As + 6A+Bs$

Reorder

$2s + 4 = As +Bs+ 6A$

By direct comparison:

$2s = As + Bs$

$4 = 6A$

Solving $2s = As + Bs$

Divide through by s

$2 = A + B$

Solve for A in $4 = 6A$

$\frac{4}{6} = A$

$A = \frac{4}{6}$

$A = \frac{2}{3}$

Substitute $\frac{2}{3}$ for A in $2 = A + B$

$2 = \frac{2}{3} + B$

$B = 2 - \frac{2}{3}$

LCM

$B = \frac{6 - 2}{3}$

$B = \frac{4}{3}$