Can anyone help on any of these problems

[taronej]

Any help to any of these problems would be great!

1) What is the domain of the rational function f(x) = 4/ x^2+3x+2 ???

Simplify the expression
2) (4/3)^-3 ???


3) 5/ x^2+3x - 2/x^2-4x ????

 

[tkhunny]

You cannot receive "help" if you are not actually trying anything. What have you done. Show a problem or two that you did solve. What tools have you?

 

[skeeter]

Any help to any of these problems would be great!

1) What is the domain of the rational function f(x) = 4/ x^2+3x+2 ???

f(x) = 4/(x^2 + 3x + 2) = 4/[(x+1)(x+2)]

... the domain of f(x) is all real numbers except those two values of x that will make f(x) undefined. your job is to determine those two x-values.

Simplify the expression
2) (4/3)^-3 ???

(4/3)^(-3) = (3/4)^(3) = (3^3)/(4^3) = ?

3) 5/ x^2+3x - 2/x^2-4x ????

5/(x^2+3x) - 2/(x^2-4x) = 5/[x(x+3)] - 2/[x(x-4)]

to combine the fractions, you need a common denominator ... x(x+3)(x-4)

5(x-4)/[x(x+3)(x-4)] - 2(x+3)/[x(x+3)(x-4)] = [5(x-4) - 2(x+3)]/[x(x+3)(x-4)]

I'll let you finish up.

 

[Denis]

5/ x^2+3x - 2/x^2-4x ????

To start with, you need BRACKETS: 5 / (x^2 + 3x) - 2 / (x^2 - 4x)

Suggestion: doing it this way is sometimes easier (less confusing):

let a = x^2 + 3x and b = x^2 - 4x ; then expression becomes:
5 / a - 2 / b
so CD becomes ab, and expression becomes:
(5b - 2a) / ab

Now substitute back in:
[5(x^2 - 4x) - 2(x^2 + 3x)] / [(x^2 + 3x)(x^2 - 4x)]

Simplify that and you'll end up with (3x - 26) / [x(x + 3)(x - 4)]

 

[taronej]

thanks

thanks for all the great help! Its got my started so i could finish the problems!!