What is expand (4i-3)/((iz+4)*(z-3)) ?

The solution to expand (4i-3)/((iz+4)*(z-3)) is 4/(16+z^2)+i(16+3z)/((-3+z)(16+z^2))

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expand (4i-3)/((iz+4)*(z-3))

expand

\frac{4 i - 3}{( i z + 4 ) \cdot ( z - 3 )}

\frac{4}{16 + z ^{2}} + i \frac{16 + 3 z}{( - 3 + z ) ( 16 + z ^{2} )}

Solution steps

\frac{4 i - 3}{( i z + 4 ) ( z - 3 )}

Expand

(i z + 4) (z - 3) : i z^{2} - 3 i z + 4 z - 12

= \frac{4 i - 3}{i z ^{2} - 3 i z + 4 z - 12}

Rationalize

\frac{4 i - 3}{i z ^{2} - 3 i z + 4 z - 12} : \frac{4 z ^{2} - 24 z + i ( 3 z ^{2} + 7 z - 48 ) + 36}{z ^{4} - 6 z ^{3} + 25 z ^{2} - 96 z + 144}

= \frac{4 z ^{2} - 24 z + 36 + i ( 3 z ^{2} + 7 z - 48 )}{z ^{4} - 6 z ^{3} + 25 z ^{2} - 96 z + 144}

Rewrite

\frac{4 z ^{2} - 24 z + 36 + i ( 3 z ^{2} + 7 z - 48 )}{z ^{4} - 6 z ^{3} + 25 z ^{2} - 96 z + 144}

in standard complex form:

\frac{4}{z ^{2} + 16} + \frac{3 z + 16}{( z - 3 ) ( z ^{2} + 16 )} i

= \frac{4}{z ^{2} + 16} + \frac{3 z + 16}{( z - 3 ) ( z ^{2} + 16 )} i

(y^{2} + 2 y) d x - x^{2} d y

e^{2 t} (e^{t} y + 2 e^{t} y^{'} (t) + e^{t} y^{''} (t))

(1 - y) e^{y} \frac{d y}{d x} + \frac{y ^{2}}{x ln ( x )}

\frac{( s + 2 ) e ^{- s}}{s ( s ^{2} + 4 s + 3 )}

\frac{1}{( 1 + x ) ^{3}}

What is expand (4i-3)/((iz+4)*(z-3)) ?
The solution to expand (4i-3)/((iz+4)*(z-3)) is 4/(16+z^2)+i(16+3z)/((-3+z)(16+z^2))