What is expand (2(a-1)(2a^2+2a-3))/(3a^2) ?

The solution to expand (2(a-1)(2a^2+2a-3))/(3a^2) is (4a)/3-(10)/(3a)+2/(a^2)

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expand (2(a-1)(2a^2+2a-3))/(3a^2)

expand

\frac{2 ( a - 1 ) ( 2 a ^{2} + 2 a - 3 )}{3 a ^{2}}

\frac{4 a}{3} - \frac{10}{3 a} + \frac{2}{a ^{2}}

Solution steps

\frac{2 ( a - 1 ) ( 2 a ^{2} + 2 a - 3 )}{3 a ^{2}}

Expand

2 (a - 1) (2 a^{2} + 2 a - 3) : 4 a^{3} - 10 a + 6

= \frac{4 a ^{3} - 10 a + 6}{3 a ^{2}}

Apply the fraction rule:

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

\frac{4 a ^{3} - 10 a + 6}{3 a ^{2}} = \frac{4 a ^{3}}{3 a ^{2}} - \frac{10 a}{3 a ^{2}} + \frac{6}{3 a ^{2}}

= \frac{4 a ^{3}}{3 a ^{2}} - \frac{10 a}{3 a ^{2}} + \frac{6}{3 a ^{2}}

Cancel

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

= \frac{4 a}{3} - \frac{10 a}{3 a ^{2}} + \frac{6}{3 a ^{2}}

Cancel

\frac{10 a}{3 a ^{2}} : \frac{10}{3 a}

= \frac{4 a}{3} - \frac{10}{3 a} + \frac{6}{3 a ^{2}}

Divide the numbers:

\frac{6}{3} = 2

= \frac{4 a}{3} - \frac{10}{3 a} + \frac{2}{a ^{2}}

\frac{( x - 1 ) x + 5}{2}

2 (\frac{4}{e ^{4}} + \frac{4}{e ^{16}} + \frac{4}{e ^{36}})

\frac{2 w ^{2} - 13 w + 21}{( w + 2 ) ( w - 6 )}

\frac{( 1 - u ) ^{3}}{3}

x (\frac{( 7 - x ) ^{2}}{18} - \frac{1}{2})

What is expand (2(a-1)(2a^2+2a-3))/(3a^2) ?
The solution to expand (2(a-1)(2a^2+2a-3))/(3a^2) is (4a)/3-(10)/(3a)+2/(a^2)