SOLUTION: Hello can someone show me how to find the domain of the rational function f(x) = x^2 + 3x -40 / x^2

SOLUTION: Hello can someone show me how to find the domain of the rational function f(x) = x^2 + 3x -40 / x^2 - 10x +24

Question 90414: Hello can someone show me how to find the domain of the rational function
f(x) = x^2 + 3x -40 / x^2 - 10x +24
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Set the denominator equal to zero:

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-10, and c=24

Negate -10 to get 10

Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

This since and both make the denominator equal to zero, this means that and are restricted from the domain. So the domain is the element of all real numbers, excluding and .
RELATED QUESTIONS
Can someone please explain to me how to do this problem? Find the domain of the... (answered by jim_thompson5910)

Find the domain of the rational function: f(x) = (2x^2 - 4) / (3x^2 + 6x -... (answered by funmath)

Find the domain of the rational function f(x)=2x^2-4/3x^2+6x-72 (answered by solver91311)

Find the domain of the rational function f(x) = (x^3 + 2x^2 + x + 1)/(x^2 + 3x +... (answered by rapaljer)

Hello, Can someone please help me find the domain of this rational function?: f(x)=... (answered by rothauserc)

Please show me step by step how to find the functin values for the following function:... (answered by tommyt3rd)

Can someone please help me find the domain of the rational function:... (answered by Alan3354)

how would you factor out this rational function and find the domain, and simplify it to... (answered by Earlsdon)

CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: FIND THE DOMAIN OF THE RATIONAL... (answered by midwood_trail)