SOLUTION: Hey, I need help with identities in chapter 6 lesson 6 of my book entitled Rational Expressions and Equations it says as follows: Equations that are true for all acceptable replace

Algebra ->  Rational-functions -> SOLUTION: Hey, I need help with identities in chapter 6 lesson 6 of my book entitled Rational Expressions and Equations it says as follows: Equations that are true for all acceptable replace      Log On


   

Question 119617: Hey, I need help with identities in chapter 6 lesson 6 of my book entitled Rational Expressions and Equations it says as follows: Equations that are true for all acceptable replacements of the variable are identities. Determine which equations areidenties.
problem as follows: xsquared + 6x - 16/ x-2 = x + 8
I also need help with solving rational expressions.
This is algebra 2
Thank you so much
I can realy use the help I need to bring up my grade cause I am realy worried about my G.P.A. because I want to get into a very good college.
Thanks again
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%5E2%2B6x-16%29%2F%28x-2%29=x%2B8 Start with the given equation. Note: since x%3C%3E2 since that will make the denominator equal to zero

%28%28x%2B8%29%28x-2%29%29%2F%28x-2%29=x%2B8 Factor x%5E2%2B6x-16 to get %28x%2B8%29%28x-2%29


%28x%2B8%29%28x-2%29%2F%28x-2%29=x%2B8 Combine the fractions


%28x%2B8%29cross%28%28x-2%29%29%2Fcross%28%28x-2%29%29=x%2B8 Cancel like terms


x%2B8=x%2B8 Simplify



x=x%2B8-8Subtract 8 from both sides


x-x=8-8 Subtract x from both sides


0x=8-8 Combine like terms on the left side


0x=0 Combine like terms on the right side


0=0 Simplify

Since this equation is always true for any x value, this means %28x%5E2%2B6x-16%29%2F%28x-2%29=x%2B8 is an identity and x can equal any number except 2.