Solving rational expressions

[czagara]

(2X+5) / (X+1) - (3X) / (X^2 + X) = 2

Here is what I came up with so far:

LCD: X(X+1)

2X^2 + 5x - 3x =2X^2 + 2x

2X^2 + 2X = 2X^2 + 2x

Is that right?

My book says the answer is all real numbers except 0, and -1

 

[mmm4444bot]

… 2X^2 + 2X = 2X^2 + 2x

Is that right? … It's good, so far.

Did you notice that the expressions are identical on each side of the equal sign, in your last result?

So, any Real number for x will satisfy this equation.

We need to remember that the factors x and x + 1 appear in denominators in the original equation.

So, any value of x that causes a denominator to evaluate to zero must be excluded from the solution set.

This is why the solution set is all Real numbers except x = 0 and x = -1.