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)

Algebra ->  Polynomials-and-rational-expressions -> 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)      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Let's factor out x%5E3%2B7x%5E2%2B12x which is the denominator on the left side.

x%5E3%2B7x%5E2%2B12x

x%28x%5E2%2B7x%2B12%29

x%28x%2B3%29%28x%2B4%29

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

x%2F%28x%5E3%2B7x%5E2%2B12x%29+=+x%2F%28x%28x%2B3%29%28x%2B4%29%29





This means that x(x+5) will go where the question mark is.

Answer by MathTherapy(10552) About Me  (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