Answer:
b = [tex]\frac{8a-55}{5-a}[/tex]
Step-by-step explanation:
To clear the radicals square both sides
[tex]\frac{1}{6-a}[/tex] = [tex]\frac{8+b}{b-7}[/tex] ( cross- multiply )
(6 - a)(8 + b) = b - 7 ← expand factors on left using FOIL
48 + 6b - 8a - ab = b - 7 ( subtract 48 from both sides )
6b - 8a - ab = b - 55 ( add 8a to both sides )
6b - ab = b - 55 + 8a ( subtract b from both sides )
6b - ab - b = 8a - 55, that is
5b - ab = 8a - 55 ← factor out b from each term on the left side )
b(5 - a) = 8a - 55 ← divide both sides by (5 - a)
b = [tex]\frac{8a-55}{5-a}[/tex]
