What is expand ((a^2+4)*(3a^2-4))/(4a^2) ?

The solution to expand ((a^2+4)*(3a^2-4))/(4a^2) is (3a^2)/4+2-4/(a^2)

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expand ((a^2+4)*(3a^2-4))/(4a^2)

expand

\frac{( a ^{2} + 4 ) \cdot ( 3 a ^{2} - 4 )}{4 a ^{2}}

\frac{3 a ^{2}}{4} + 2 - \frac{4}{a ^{2}}

Solution steps

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

Expand

(a^{2} + 4) (3 a^{2} - 4) : 3 a^{4} + 8 a^{2} - 16

= \frac{3 a ^{4} + 8 a ^{2} - 16}{4 a ^{2}}

Apply the fraction rule:

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

\frac{3 a ^{4} + 8 a ^{2} - 16}{4 a ^{2}} = \frac{3 a ^{4}}{4 a ^{2}} + \frac{8 a ^{2}}{4 a ^{2}} - \frac{16}{4 a ^{2}}

= \frac{3 a ^{4}}{4 a ^{2}} + \frac{8 a ^{2}}{4 a ^{2}} - \frac{16}{4 a ^{2}}

Cancel

\frac{3 a ^{4}}{4 a ^{2}} : \frac{3 a ^{2}}{4}

= \frac{3 a ^{2}}{4} + \frac{8 a ^{2}}{4 a ^{2}} - \frac{16}{4 a ^{2}}

Cancel

\frac{8 a ^{2}}{4 a ^{2}} : 2

= \frac{3 a ^{2}}{4} + 2 - \frac{16}{4 a ^{2}}

Divide the numbers:

\frac{16}{4} = 4

= \frac{3 a ^{2}}{4} + 2 - \frac{4}{a ^{2}}

\frac{1}{( 1 + e ^{x} ) e ^{- x}}

2 π (\frac{π}{8} ln (2) - \frac{3}{4})

\frac{1}{( 2 n + 1 ) ^{2}}

\frac{1}{( x ^{2} - x + 1 ) ( x ^{2} + x + 1 )}

2^{b (x - c)^{2}}

What is expand ((a^2+4)*(3a^2-4))/(4a^2) ?
The solution to expand ((a^2+4)*(3a^2-4))/(4a^2) is (3a^2)/4+2-4/(a^2)