Answer:
The solution to the equation is:
Option c. b=0 and b=4
Step-by-step explanation:
5 / (3b^3-2b^2-5) = 2 / (b^3-2)
Cross multiplication:
5(b^3-2)=2(3b^3-2b^2-5)
Applying distributive property both sides of the equation to eliminate the parentheses:
5(b^3)-5(2)=2(3b^3)-2(2b^2)-2(5)
Multiplying:
5b^3-10=6b^3-4b^2-10
Passing all the terms to the right side of the equation: Subtracting 5b^3 and adding 6 both sides of the equation:
5b^3-10-5b^3+10=6b^3-4b^2-10-5b^3+10
Adding like terms:
0=b^3-4b^2
b^3-4b^2=0
Getting common factor b^2 on the left side of the equation:
b^2 (b^3/b^2-4b^2/b^2)=0
b^2 (b-4) = 0
Two solutions:
(1) b^2=0
Solving for b: Square root both sides of the equation:
sqrt(b^2)=sqrt(0)
Square root:
b=0
(2) b-4=0
Solving for b: Adding 4 both sides of the equation:
b-4+4=0+4
Adding like terms:
b=4
The solution of the equation is: b=0 and b=4 (Option c)
