SOLUTION: {{{ 3/(x-2) + 5/(x+2) = 4x^2/(x^2-4) }}} I am trying to solve this problem however I do not even know how to begin to work it out. How do I solve this problem?

Question 132602This question is from textbook Algebra II
:
I am trying to solve this problem however I do not even know how to begin to work it out. How do I solve this problem? This question is from textbook Algebra II

Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Factor to get

Notice how the LCD is

Multiply both sides by the LCD . Doing this will eliminate every fraction.

Distribute and multiply. Notice every denominator has been canceled out.

Distribute again

Combine like terms

Subtract from both sides.

Rearrange the terms

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

Since we have a repeating answer, our only answer is

---------------------------------------------------------------------

Answer:

So the solution is

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The first step is to recognize that is the difference of two squares that factors thusly: . So, . That means that you can re-write your equation like this:

Now you should be able to see that the lowest common denominator for the three rational expressions (fractions) that comprise your equation is .

So:

Now that all of the denominators are the same, you can just add the numerators together, just like any other fraction addition problem. First, distribute and remove parentheses:

And add the opposite of the right hand side of the equation to both sides:

Now collect like terms:

Now is a good time to note that either 2 or -2 would make the denominator 0, if either of these numbers comes up as a possible solution to the problem, we have to exclude those values. The solution set of an equation cannot have an element that makes any expression that is part of the equation undefined.

Keeping that in the back of our mind, recognize that if and only if and . That means that the solution to our equation can be found by setting the numerator equal to zero and solving the quadratic for all possible values of x.

Divide by -4:

Since and , we can say that . Therefore or so or

Since neither of these results is 2 or -2, we don't have to worry about a zero denominator. Therefore the roots of the equation consist of the value 1 with a multiplicity of 2, which is the same as saying there are two real and identical roots.
RELATED QUESTIONS
I am struggling with this problem and do not know how to solve it. Please help if you... (answered by Edwin McCravy)
I do not know how to even begin to solve the following inequality:... (answered by Edwin McCravy)
With these two problems, I am very confused, because math is not my thing, and I do not... (answered by ankor@dixie-net.com,mangopeeler07)
This is actually solving a problem that is quadratic in form. I am having lots of... (answered by Earlsdon)
I made my own problem for fun and am trying to solve it: x^2y + 5 = 17 While I was... (answered by josgarithmetic)
Please help me solve this problem 6x/(x^2-4)+3/(2-x) I am trying to understand the steps... (answered by josgarithmetic,MathTherapy)
i know how to do algebra problems using the addition method, however i can not get the... (answered by Edwin McCravy,MathTherapy)
{{{sqrt X+2 - sqrt X-3 = sqrt X-6}}} This is the problem I am trying to work out. I... (answered by ankor@dixie-net.com)
I am having a very difficult time trying to reach the solution to this problem. I am to (answered by Alan3354,Mathtut)