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

The solution to (2a(a+4))/a-(2a(3a-4))/(2a) is -a+12

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simplify (2a(a+4))/a-(2a(3a-4))/(2a)

simplify

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

- a + 12

Solution steps

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

\frac{2 a ( a + 4 )}{a} = 2 (a + 4)

\frac{2 a ( 3 a - 4 )}{2 a} = 3 a - 4

= 2 (a + 4) - (3 a - 4)

Apply the distributive law:

- (a - b) = - a + b

- (3 a - 4) = - 3 a + 4

= 2 (a + 4) - 3 a + 4

Expand

2 (a + 4) : 2 a + 8

= 2 a + 8 - 3 a + 4

Group like terms

= 2 a - 3 a + 8 + 4

Add similar elements:

2 a - 3 a = - a

= - a + 8 + 4

Add the numbers:

8 + 4 = 12

= - a + 12

10 x^{- 2}

(m + 3 n)^{2}

9 - \frac{9}{4}

What is (2a(a+4))/a-(2a(3a-4))/(2a) ?
The solution to (2a(a+4))/a-(2a(3a-4))/(2a) is -a+12