Question

Divide the expressions:
x + 1 / x + 2 ÷ 3x / x − 4.

Answer 1

Remember,
`(a)/(b)/ (c)/(d)=(a)/(b)*(d)/(c)=(a*c)/(b*d)`

Then,

`(x+1)/(x+2)/(3x)/(x-4)=(x+1)/(x+2)*(x-4)/(3x)=((x+1)(x-4))/(3x(x+2))=(x^2-3x-4)/(3x^2+6x)`,

Now, using long division of polynomies we have that

`(x^2-3x-4)/(3x^2+6x)=(1)/(3)-(5x+4)/(3x^2+6x)`