Answer:
[tex]\frac{4}{b}=\frac{8c^9}{6-3c^9a}[/tex]
Step-by-step explanation:
Given the expression
[tex]a+\frac{2b}{3}=\frac{2}{c^9}[/tex]
subtract a from both sides
[tex]a+\frac{2b}{3}-a=\frac{2}{c^9}-a[/tex]
Simplify
[tex]\frac{2b}{3}=\frac{2}{c^9}-a[/tex]
Multiply both sides by 3
[tex]\frac{3\cdot \:2b}{3}=3\cdot \frac{2}{c^9}-3a[/tex]
Simplify
[tex]2b=\frac{6}{c^9}-3a[/tex]
Divide both sides by 2
[tex]\frac{2b}{2}=\frac{\frac{6}{c^9}}{2}-\frac{3a}{2}[/tex]
Simplify
[tex]b=\frac{6-3ac^9}{2c^9}[/tex]
Calculating 4/b
[tex]\frac{4}{b}=\frac{4}{\frac{6-3ac^9}{2c^9}}[/tex] ∵ [tex]b=\frac{6-3ac^9}{2c^9}[/tex]
[tex]\frac{4}{b}\:=\frac{4\:\times \:\:2c^9}{6-3ac^9}[/tex]
[tex]\frac{4}{b}=\frac{8c^9}{6-3c^9a}[/tex]
Therefore, we conclude that:
[tex]\frac{4}{b}=\frac{8c^9}{6-3c^9a}[/tex]
