What is (4k)/((0.5s+1)(5s+1))+1/(s+1) ?

The solution to (4k)/((0.5s+1)(5s+1))+1/(s+1) is (4ks+4k+2.5s^2+5.5s+1)/((s+1)(5s+1)(0.5s+1))

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simplify (4k)/((0.5s+1)(5s+1))+1/(s+1)

simplify

\frac{4 k}{( 0.5 s + 1 ) ( 5 s + 1 )} + \frac{1}{s + 1}

\frac{4 k s + 4 k + 2.5 s ^{2} + 5.5 s + 1}{( s + 1 ) ( 5 s + 1 ) ( 0.5 s + 1 )}

Solution steps

\frac{4 k}{( 0.5 s + 1 ) ( 5 s + 1 )} + \frac{1}{s + 1}

Least Common Multiplier of

(0.5 s + 1) (5 s + 1), s + 1 : (s + 1) (5 s + 1) (0.5 s + 1)

Adjust Fractions based on the LCM

= \frac{4 k ( s + 1 )}{( s + 1 ) ( 5 s + 1 ) ( 0.5 s + 1 )} + \frac{( 5 s + 1 ) ( 0.5 s + 1 )}{( s + 1 ) ( 5 s + 1 ) ( 0.5 s + 1 )}

Apply the fraction rule:

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

= \frac{4 k ( s + 1 ) + ( 5 s + 1 ) ( 0.5 s + 1 )}{( s + 1 ) ( 5 s + 1 ) ( 0.5 s + 1 )}

Simplify

4 k (s + 1) + (5 s + 1) (0.5 s + 1) : 4 k s + 4 k + 2.5 s^{2} + 5.5 s + 1

= \frac{4 k s + 4 k + 2.5 s ^{2} + 5.5 s + 1}{( s + 1 ) ( 5 s + 1 ) ( 0.5 s + 1 )}

\frac{2 ( x + h ) ^{3}}{3}

(2 e^{t} + 3 t)^{2}

\frac{( x + 1 ) ( x - 1 )}{x + 4}

(x + 1) \times ln^{2} (x + 1)

sec (2 (arcsec (\frac{25}{7}) + 2 πn))

What is (4k)/((0.5s+1)(5s+1))+1/(s+1) ?
The solution to (4k)/((0.5s+1)(5s+1))+1/(s+1) is (4ks+4k+2.5s^2+5.5s+1)/((s+1)(5s+1)(0.5s+1))