What is (4-2j)/(2+j)+(2j)/(1-j) ?

The solution to (4-2j)/(2+j)+(2j)/(1-j) is (4j^2-2j+4)/((j+2)(-j+1))

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simplify (4-2j)/(2+j)+(2j)/(1-j)

simplify

\frac{4 - 2 j}{2 + j} + \frac{2 j}{1 - j}

\frac{4 j ^{2} - 2 j + 4}{( j + 2 ) ( - j + 1 )}

Solution steps

\frac{4 - 2 j}{2 + j} + \frac{2 j}{1 - j}

Least Common Multiplier of

2 + j, 1 - j : (j + 2) (- j + 1)

Adjust Fractions based on the LCM

= \frac{( 4 - 2 j ) ( - j + 1 )}{( j + 2 ) ( - j + 1 )} + \frac{2 j ( j + 2 )}{( j + 2 ) ( - j + 1 )}

Apply the fraction rule:

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

= \frac{( 4 - 2 j ) ( - j + 1 ) + 2 j ( j + 2 )}{( j + 2 ) ( - j + 1 )}

Simplify

(4 - 2 j) (- j + 1) + 2 j (j + 2) : 4 j^{2} - 2 j + 4

= \frac{4 j ^{2} - 2 j + 4}{( j + 2 ) ( - j + 1 )}

\frac{x}{a ^{2} - a x} + \frac{a + x}{a x} + \frac{a}{a x - x ^{2}}

lo g_{10} (\frac{x y ^{7}}{z ^{3}})

(x + 4) (x + 4)

\frac{100}{16}

\frac{8}{2}

What is (4-2j)/(2+j)+(2j)/(1-j) ?
The solution to (4-2j)/(2+j)+(2j)/(1-j) is (4j^2-2j+4)/((j+2)(-j+1))