What is (12a^3-3a)/(12a^3+6a^2) ?

The solution to (12a^3-3a)/(12a^3+6a^2) is (2a-1)/(2a)

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simplify (12a^3-3a)/(12a^3+6a^2)

simplify

\frac{12 a ^{3} - 3 a}{12 a ^{3} + 6 a ^{2}}

\frac{2 a - 1}{2 a}

Solution steps

\frac{12 a ^{3} - 3 a}{12 a ^{3} + 6 a ^{2}}

Factor

12 a^{3} - 3 a : 3 a (2 a + 1) (2 a - 1)

= \frac{3 a ( 2 a + 1 ) ( 2 a - 1 )}{12 a ^{3} + 6 a ^{2}}

Factor

12 a^{3} + 6 a^{2} : 6 a^{2} (2 a + 1)

= \frac{3 a ( 2 a + 1 ) ( 2 a - 1 )}{6 a ^{2} ( 2 a + 1 )}

Cancel the common factor:

2 a + 1

= \frac{3 a ( 2 a - 1 )}{6 a ^{2}}

Factor the number:

6 = 3 \cdot 2

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

Cancel the common factor:

3

= \frac{a ( 2 a - 1 )}{2 a ^{2}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

a^{2} = aa

= \frac{a ( 2 a - 1 )}{2 aa}

Cancel the common factor:

a

= \frac{2 a - 1}{2 a}

4 (3) - 5 (5) = 8

2 x^{2} + 2 = 2 x

3 (y + 2) - y = 2 (y - 1) + 5

7 x + 21

14 x = 12 x + 3

What is (12a^3-3a)/(12a^3+6a^2) ?
The solution to (12a^3-3a)/(12a^3+6a^2) is (2a-1)/(2a)