[tex]\sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex] or [tex]\sf \dfrac{54a-52}{24}[/tex]
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[tex]\sf \rightarrow 7\left(\dfrac{5}{14}a-\dfrac{5}{21}\right)-\dfrac{1}{12}\left(3a+6\right)[/tex]
use distributive method
[tex]\sf \rightarrow \dfrac{5a}{2}-\dfrac{5}{3}-\dfrac{a}{4}-\dfrac{1}{2}[/tex]
group terms
[tex]\rightarrow \sf \rigtharrow \dfrac{5a}{2}-\dfrac{a}{4}-\dfrac{5}{3}-\dfrac{1}{2}[/tex]
make the denominators same
[tex]\rightarrow \sf \rigtharrow \dfrac{2(5a)}{4}-\dfrac{a}{4}-\dfrac{2(5)}{6}-\dfrac{3(1)}{6}[/tex]
simplify
[tex]\rightarrow \sf \rigtharrow \dfrac{10a-a}{4}-\dfrac{10+3}{6}[/tex]
answer in separate constants
[tex]\rightarrow \sf \dfrac{9a}{4}-\dfrac{13}{6}[/tex]
make the denominators same
[tex]\rightarrow \sf \dfrac{6(9a)}{24}-\dfrac{4(13)}{24}[/tex]
simplify
[tex]\rightarrow \sf \dfrac{54a}{24}-\dfrac{52}{24}[/tex]
join both fractions
[tex]\rightarrow \sf \dfrac{54a-52}{24}[/tex]
Answer:
[tex]\boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]
Step-by-step explanation:
[tex]7(\dfrac{5a}{14} - \dfrac{5}{21} ) - \dfrac{(3a + 6)}{12}[/tex]
Step-1: Simplify the distributive property
⇒ [tex]\dfrac{35a}{14} - \dfrac{35}{21} - \dfrac{(3a + 6)}{12}[/tex]
Step-2: Make common denominators
⇒ [tex]\dfrac{35a \times 3}{14 \times 3} - \dfrac{35 \times 2}{21 \times 2} - \dfrac{7 \times (3a + 6)}{12 \times 7}[/tex]
⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{7 \times (3a + 6)}{84}[/tex]
Step-3: Simplify the distributive property
⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a + 42}{84}[/tex]
Step-4: Rewrite (21a + 42)/84 in a different way
⇒ [tex]\dfrac{210a}{84} - \dfrac{140}{84} - \dfrac{21a}{84} + \dfrac{42}{84}[/tex]
Step-5: Add/Subtract if necessary
⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}}[/tex]
Step-6: Simplify the fractions
⇒ [tex]{\dfrac{189a}{84} - \dfrac{98}{84}} = {\dfrac{9a}{4} - \dfrac{49}{42}} = \boxed{\dfrac{9a}{4} - \dfrac{7}{6}}[/tex]