Question

7(5/14a-5/21)-1/12(3a+6)

Answer 1

`\boxed{(9a)/(4) - (7)/(6)}`

Explanation:

`7((5a)/(14) - (5)/(21) ) - ((3a + 6))/(12)`

Step-1: Simplify the distributive property

⇒
`(35a)/(14) - (35)/(21) - ((3a + 6))/(12)`

Step-2: Make common denominators

⇒
`(35a * 3)/(14 * 3) - (35 * 2)/(21 * 2) - (7 * (3a + 6))/(12 * 7)`

⇒
`(210a)/(84) - (140)/(84) - (7 * (3a + 6))/(84)`

Step-3: Simplify the distributive property

⇒
`(210a)/(84) - (140)/(84) - (21a + 42)/(84)`

Step-4: Rewrite (21a + 42)/84 in a different way

⇒
`(210a)/(84) - (140)/(84) - (21a)/(84) + (42)/(84)`

Step-5: Add/Subtract if necessary

⇒
`{(189a)/(84) - (98)/(84)}`

Step-6: Simplify the fractions

⇒
`{(189a)/(84) - (98)/(84)} = {(9a)/(4) - (49)/(42)} = \boxed{(9a)/(4) - (7)/(6)}`

Answer 2

`\sf (9a)/(4)-(13)/(6)` or
`\sf (54a-52)/(24)`

======================================

`\sf \rightarrow 7\left((5)/(14)a-(5)/(21)\right)-(1)/(12)\left(3a+6\right)`

use distributive method

`\sf \rightarrow (5a)/(2)-(5)/(3)-(a)/(4)-(1)/(2)`

group terms

`\rightarrow \sf \rigtharrow (5a)/(2)-(a)/(4)-(5)/(3)-(1)/(2)`

make the denominators same

`\rightarrow \sf \rigtharrow (2(5a))/(4)-(a)/(4)-(2(5))/(6)-(3(1))/(6)`

simplify

`\rightarrow \sf \rigtharrow (10a-a)/(4)-(10+3)/(6)`

answer in separate constants

`\rightarrow \sf (9a)/(4)-(13)/(6)`

make the denominators same

`\rightarrow \sf (6(9a))/(24)-(4(13))/(24)`

simplify

`\rightarrow \sf (54a)/(24)-(52)/(24)`

join both fractions

`\rightarrow \sf (54a-52)/(24)`