SOLUTION: can someone please help me multiply? 4x-40 over x^2+10x multiplied by 3x over 10-x

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Question 81653: can someone please help me multiply?
4x-40
over
x^2+10x
multiplied by
3x
over
10-x
Found 2 solutions by rapaljer, tutorcecilia:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
%284x-40%29%2F%28x%5E2%2B10x%29 * %283x%29%2F%2810-x%29+

The first step is to factor the first numerator and denominator:
%28%284%28x-10%29%29%2F%28x%28x%2B10%29%29%29+%2A+%28%283x%29%2F%2810-x%29%29

Notice that the x factor in the first denominator and the second numerator divide out. Also, notice that the factor of (x-10) in the first numerator and the (10-x) in the second denominator are NEGATIVES of one another, so they divide out, leaving a factor of -1 in the first numerator:
%28%284%2A%28-1%29%29%2F%28x%2B10%29%29%2A+%283%2F1%29
%28-12%29%2F%28x%2B10%29+
You might also want to see additional examples and exercises on the "Math in Living Color" page of my website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Then look for "Math in Living Color." Fractions like this can then be found in all three levels, "Basic Algebra", "Intermediate Algebra," or "College Algebra." In Basic Algebra, look for Chapter 3 topics, in Intermediate Algebra look for Chapter 2 topics, and in College Algebra, the fractions are covered in Chapter 1. I hope this will be a useful reference for anyone who has trouble with a variety of topics relating to fractions. EVERYONE has trouble with fractions!!

R^2 at SCC



Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
%28%28%284x-40%29%2F%28x%5E2%2B10x%29%29%2A%28%283x%29%2F%2810-x%29%29%29
%28%28%284%29%28x-10%29%2F%28x%29%28x%2B10%29%29%2A%28%283x%29%2F%2810-x%29%29%29 [factor whrever possible]
[multiply through by (-1) to cause the expressions to match: (-1)(4)(-1)(x-10)=-4(-x+10)]
.
%28%28%28-4%29%28-x%2B10%29%2F%28x%29%28x%2B10%29%29%2A%28%283x%29%2F%2810-x%29%29%29
%28%28%28-4%29%2810-x%29%2F%28x%29%28x%2B10%29%29%2A%28%283x%29%2F%2810-x%29%29%29 [re-arrange the terms: -x+10 = 10-x which does not change the value]
.

%28%28%28-4%29%2F%28x%29%28x%2B10%29%29%2A%28%283x%29%2F%281%29%29%29 [cancel wherever possible]
%28%28%28-4%29%2F%281%29%28x%2B10%29%29%2A%28%282x%29%2F%281%29%29%29 [cancel wherever possible]
%28%28%28-8x%29%2F%28x%2B10%29%29%29%29 [if you cannot reduce or cancel any further, than multiply straight across]
.