SOLUTION: Solve the equation (4w-1)/(3w+6)-(w-1)/3=(w-1)/w+2

Question 121085: Solve the equation (4w-1)/(3w+6)-(w-1)/3=(w-1)/w+2
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Step 1 is to put your variable on one side, so add to both sides of the equation

Now we need a common denominator. Notice that factors to and those two factors are the other two denominators. Therefore, is our lowest common denominator.

We can leave the first term alone, but the second term has to be multiplied by and the third term must be multiplied by

Now is a good time to note that since is a factor in the denominator, we need to exclude from the solution set because that would make a denominator or denominators in the original equation go to zero.

Multiply the binomial factors and distribute the 3

Collect terms

Factor the difference of two squares:

So, or , in other words, or . But remember, we have to exclude from the solution set because that value makes the original equation undefined. In the process of applying the common denominator, we introduced the square of the variable and that process introduced an extraneous root.

is the only root of the equation.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation

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

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

Foil

Multiply and to get

Distribute

Get everything to the left side

Factor the left side

Now set each factor equal to zero:

or

Now solve for w for each factor:

or

So our possible solutions are:

or

However, if we plug in into the original equation, we'll get a zero denominator. So is not a possible solution

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

Answer:

So our solution is

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