multiply and simplify: x^2+4x+3/x^2+4x+4 5x+10/x+3

[jake_k2011]

Hello i'm having trouble with a few problems and would love some help

Perform the multiplication and simplify:
x^2+4x+3/x^2+4x+4 5x+10/x+3

Simplify the rational expression
t^3-216/t^2-36

Find all real solutions of the equation.
X^3-5x^2-5x+25=0

Perform the indicated operation.
1/x-1/6 / x-6

Thank you very much

 

[Loren]

Re: a few problems

The first thing you need to do is to learn to use parenthesis to clarify what you mean.

Hello i'm having trouble with a few problems and would love some help

Perform the multiplication and simplify:
x^2+4x+3/x^2+4x+4 5x+10/x+3 <<< means \(\displaystyle x^2+4x+\frac{3}{x^2}+4x+4\) (space) \(\displaystyle 5x+\frac{10}{x}+3\)




Simplify the rational expression
t^3-216/t^2-36 <<<means \(\displaystyle t^3-\frac{216}{t^2}-36\)


Find all real solutions of the equation.
X^3-5x^2-5x+25=0 <<< This is good. No parenthesis needed. Just factor out x^2 from the first two terms and a -5 from the second two, then factor using the grouping method and go from there.


Perform the indicated operation.
1/x-1/6 / x-6 <<< I think you mean (1/x - 1/6)/(x-6) which is \(\displaystyle \frac{\frac{1}{x}-\frac{1}{6}}{x-6}\). If that is what you mean, one approach is to start by multiplying both numerator and denominator by -6x.

Thank you very much