SOLUTION: rewrite the rational expression as an equivalent rational expression with the given denominator x/x^3+7x^2+12x=?/x(x+5)(x+3)(x+4)

Question 1059713: rewrite the rational expression as an equivalent rational expression with the given denominator
x/x^3+7x^2+12x=?/x(x+5)(x+3)(x+4)
Found 2 solutions by jim_thompson5910, MathTherapy:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's factor out which is the denominator on the left side.

Looking at that factorization and comparing it to x(x+5)(x+3)(x+4), which is the denominator on the right side, all we're missing is (x+5).

So multiply top and bottom of the fraction on the left by (x+5) to get

This means that x(x+5) will go where the question mark is.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
rewrite the rational expression as an equivalent rational expression with the given denominator
x/x^3+7x^2+12x=?/x(x+5)(x+3)(x+4)

-------------- Factoring left denominator
----- The binomial: "x + 5" is needed in the LEFT-DENOMINATOR to be equivalent to the right-denominator. It MUST be included in the LEFT-NUMERATOR as well
---- Equivalency is NOW obtained
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