SOLUTION: Rational Expressions and Equations Reduce to the lowest terms: 18x2 + 48x + 32 3x + 4 Divide the algebric expression: x - 2 / x - 2 x + 2 5

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Rational Expressions and Equations Reduce to the lowest terms: 18x2 + 48x + 32 3x + 4 Divide the algebric expression: x - 2 / x - 2 x + 2 5       Log On


   

Question 149578: Rational Expressions and Equations
Reduce to the lowest terms:
18x2 + 48x + 32
3x + 4

Divide the algebric expression:
x - 2 / x - 2
x + 2 5


Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1

%2818x%5E2%2B48x%2B32%29%2F%283x%2B4%29 Start with the given expression.


%282%283x%2B4%29%283x%2B4%29%29%2F%283x%2B4%29 Factor 18x%5E2%2B48x%2B32 to get 2%283x%2B4%29%283x%2B4%29.


%282highlight%28%283x%2B4%29%29%283x%2B4%29%29%2Fhighlight%28%283x%2B4%29%29 Highlight the common terms.


%282cross%28%283x%2B4%29%29%283x%2B4%29%29%2Fcross%28%283x%2B4%29%29 Cancel out the common terms.


2%283x%2B4%29 Simplify.


6x%2B8 Distribute


So %2818x%5E2%2B48x%2B32%29%2F%283x%2B4%29 simplifies to 6x%2B8.


In other words, %2818x%5E2%2B48x%2B32%29%2F%283x%2B4%29=6x%2B8 where x%3C%3E-4%2F3




# 2



%28%28x-2%29%2F%28x%2B2%29%29%2F%28%28x-2%29%2F%285%29%29 Start with the given expression.


%28%28x-2%29%2F%28x%2B2%29%29%28%285%29%2F%28x-2%29%29 Multiply the first fraction %28x-2%29%2F%28x%2B2%29 by the reciprocal of the second fraction %28x-2%29%2F%285%29.



%285%28x-2%29%29%2F%28%28x%2B2%29%28x-2%29%29 Combine the fractions.


%285highlight%28x-2%29%29%2F%28%28x%2B2%29highlight%28x-2%29%29 Highlight the common terms.


%285cross%28x-2%29%29%2F%28%28x%2B2%29cross%28x-2%29%29 Cancel out the common terms.


%285%29%2F%28x%2B2%29 Simplify.


So %28%28x-2%29%2F%28x%2B2%29%29%2F%28%28x-2%29%2F%285%29%29 simplifies to %285%29%2F%28x%2B2%29.


In other words, %28%28x-2%29%2F%28x%2B2%29%29%2F%28%28x-2%29%2F%285%29%29=%285%29%2F%28x%2B2%29 where x%3C%3E-2 or x%3C%3E2