Question

What is the solution for the equation StartFraction 5 Over 3 b cubed minus 2 b squared minus 5 EndFraction = StartFraction 2 Over b cubed minus 2 EndFraction?

Answer 1

c

Explanation:

Answer 2

The solutions are:

`b=0,\:b=4`

Explanation:

Considering the expression

• 
  `(5)/(3b^3-2b^2-5)=(2)/(b^3-2)`

Solving the expression

`(5)/(3b^3-2b^2-5)=(2)/(b^3-2)`

`\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}(a)/(b)=(c)/(d)\mathrm{\:then\:}a\cdot \:d=b\cdot \:c`

`5\left(b^3-2\right)=\left(3b^3-2b^2-5\right)\cdot \:2`

`5b^3-10=6b^3-4b^2-10`

`\mathrm{Switch\:sides}`

`6b^3-4b^2-10=5b^3-10`

`6b^3-4b^2-10+10=5b^3-10+10`

`6b^3-4b^2=5b^3`

`\mathrm{Subtract\:}5b^3\mathrm{\:from\:both\:sides}`

`6b^3-4b^2-5b^3=5b^3-5b^3`

`b^3-4b^2=0`

`Using\:the\:Zero\:Factor\:Principle:`
`if\:\mathrm ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)`

So,

`b=0,b-4=0`

`b=0,b=4`

Therefore, the solutions are:

`b=0,\:b=4`