Simplifying Rational Expressions?

Yeah... I don't understand my tutor homework, yes I'll go after it with her tomorrow but I wanna try and get the concept of it first...


Total of 29 questions (lol), I just need the concept so just 3. The answer is not as important as explaining... Help!





1. a+b / a^2 - b^2








2. c^2 - 4 / (c + 2)^2








3. 7a^3b^2 / 21a^2b + 49ab^3








Please explain!

Simplifying Rational Expressions?
hi,


(1)


a+b / a² - b² --%26gt; factor the numerator and denominator.


a+b/(a-b)(a+b) --%26gt; since the common factor is a+b cancel it.


1/a-b --%26gt; answer.





(2) the same procedure in #1.


c²- 4 / (c + 2)²


(c-2)(c+2)/(c+2) (c+2) --%26gt; common factor is c+2.


c-2/c+2 --%26gt; answer.





(3).


7a^3b² / 21a²b + 49ab^3


7a^3b² / 7ab(3a+7b²) --%26gt; factor %26amp; look for common factor.


a²b(7ab) / 7ab(3a+7b²) --%26gt; common factor is 7ab.


a²b / 3a+7b² --%26gt; answer.
Reply:Find the common terms in denom and numerator


1. a+b/a^2- b^2 = a+b/(a+b)(a-b)


the a+b cancel out so your left with a-b


you can subsititute numbers in and a-b= a+b/a^2- b^2


2. c^2 - 4 / (c + 2)^2= (c-2)(c+2)/ (c+2)(c+2)


the c=2 cancel out so your left with (c-2)/(c+2)


3. 7a^3b^2 / 21a^2b + 49ab^3 =


7ab(a^2b)/7ab(3a+7b^2)


the 7ab cancel out so your left with (a^2b)/(3a+7b^2)
Reply:1. a+b /a^2-b^2 = a+b/aa-bb = 1+1/a-b = 2/a-b





expand on the exponent, cancel w/division





2. c^2-4/(c+2)^2 =


c^2-4 / (c+2)(c+2)= expand denominator


c^2-4/ c^2+2c+2c+4=foil


c^2-4/ c^2+4c+4 = combine like terms


-4 / 4c+4 = divide common or cancel 4's


- 1/ 4c











3. (7a^3)(b^2)/ 21a^2b+ 49ab^3=





7(a)(a)(a)(b)(b)/ 21(a)(a)(b)+49(a)(b)(b)(b)= expand





7aa/21aab+49b=cancel the b's leaving 1 in each term of the denominator





7/21b+49b= cancel the a's





7 /70b= the denominator can now be added because they have the same variable 'b' without any exponents^. and reduce=





1/10b


**Attempt to get rid of one of the variables entirely. In this case the variable 'a' .