What is (z(kz+5))/(z^4+kz^2+5.1z+0.5)+1 ?

The solution to (z(kz+5))/(z^4+kz^2+5.1z+0.5)+1 is (z^4+2z^2k+10.1z+0.5)/(z^4+kz^2+5.1z+0.5)

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simplify (z(kz+5))/(z^4+kz^2+5.1z+0.5)+1

simplify

\frac{z ( k z + 5 )}{z ^{4} + k z ^{2} + 5.1 z + 0.5} + 1

\frac{z ^{4} + 2 z ^{2} k + 10.1 z + 0.5}{z ^{4} + k z ^{2} + 5.1 z + 0.5}

Solution steps

\frac{z ( k z + 5 )}{z ^{4} + k z ^{2} + 5.1 z + 0.5} + 1

Apply the fraction rule:

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

= \frac{( z ^{4} + k z ^{2} + 5.1 z + 0.5 ) + z ( k z + 5 )}{z ^{4} + k z ^{2} + 5.1 z + 0.5}

Apply rule:

(a) = a

(z^{4} + k z^{2} + 5.1 z + 0.5) = z^{4} + k z^{2} + 5.1 z + 0.5

= \frac{z ^{4} + k z ^{2} + 5.1 z + 0.5 + z ( k z + 5 )}{z ^{4} + k z ^{2} + 5.1 z + 0.5}

Simplify

z^{4} + k z^{2} + 5.1 z + 0.5 + z (k z + 5) : z^{4} + 2 z^{2} k + 10.1 z + 0.5

= \frac{z ^{4} + 2 z ^{2} k + 10.1 z + 0.5}{z ^{4} + k z ^{2} + 5.1 z + 0.5}

\frac{( 5 x + 9 ) ( x + 3 )}{( x + 2 ) ( 4 x + 3 )}

(m^{2} n^{2} - \frac{3}{4}) (m^{2} n^{2} + \frac{1}{2})

sin^{2} (θ) (1 + cot (θ))

\frac{1}{4 \cdot π \cdot 0.02} (\frac{1}{0.65} - \frac{1}{0.75}) + \frac{1}{5}

What is (z(kz+5))/(z^4+kz^2+5.1z+0.5)+1 ?
The solution to (z(kz+5))/(z^4+kz^2+5.1z+0.5)+1 is (z^4+2z^2k+10.1z+0.5)/(z^4+kz^2+5.1z+0.5)