SOLUTION: Can someone pls help me with Simplifying Rational Expressions?, thanks! 1) <a href="http://photobucket.com" target="_blank"><img src="http://i10.photobucket.com/albums/a139/mzzu

Click here to see ALL problems on Functions

Question 29250: Can someone pls help me with Simplifying Rational Expressions?, thanks!
1)

2)

3)

Found 2 solutions by sdmmadam@yahoo.com, Earlsdon:
Answer by sdmmadam@yahoo.com(530) (Show Source):
You can put this solution on YOUR website!
Can someone pls help me with Simplifying Rational Expressions?, thanks!
1) (3a^2+15a)/(a^3-25a)
= [3a(a+5)]/[a(a^2-5^2)]
=3(a+5)/[(a+5)(a-5)] (canceling a)
(using formula (a^2-b^2)= (a+b)(a-b), here a is a and b =5)
=3/(a-5)(canceling(a+5)
Answer:(3a^2+15a)/(a^3-25a)=3/(a-5)
2)(2x^2-14x)/(x^2-10x+21)
=[2x(x-7)]/[(x-7)(x-3)]
=2x/(x-3) (cancel.. (x-7)
Answer:(2x^2-14x)/(x^2-10x+21)= 2x/(x-3)
Note: Since the nr contains the factor (x-7), usually the trick of assuming one factor in the dr as (x-7) and later trying the next factor and see if it works is one of the short cuts that will work at times!
Note: (x^2-10x+21)
= x^2+(-7x-3x)+21
= (x^2-7x)-3x+21
= x(x-7)-3x+21
= x(x-7)-3(x-7)
=xp-3p Where p=(x-7)
=p(x-3)
= (x-7)(x-3)
[(splitting the middle term as a sum of two terms in such a way that their product is the product of the square term and the constant term)
And so, -10x = (-7x) +(-3x) and (-7x)X(-3x) = +21x^2 = (x^2)X(21)]

3) (1-3x)/(3x^2+14x-5)
=(1-3x)/[(x+5)(3x-1)]
=-(3x-1)/[(x+5)(3x-1)]
(pulling out (-1) in the nr so as to get (3x-1) same as that in the dr)
=-1/(x+5) (cancel..(3x-1) )
Answer:(1-3x)/(3x^2+14x-5)=-1/(x+5)
Note: take the quadratic expression (3x^2+14x-5)in the rough work column
and factorise it as follows:
(3x^2+14x-5)
=3x^2+(15x-x)-5
splitting the middle term as a sum of two terms in such a way that their product is the product of the square term and the constant term)
And so, 14x = (15x)+(-x) so that (15x)X(-x) = -15x^2 = (3x^2)X(-5)
=(3x^2+15x)-x-5
=3x(x+5)-1(x+5)
=3xp-p where p= (x+5)
=p(3x-1)
=(x+5)(3x-1)

Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
Simplify:
1)
Factor 3a from the top and an a from the bottom.
Cancel the a's, then factor the bottom.
Cancel the common factor (a+5).

2)
Factor 2x from the top and factor the bottom.
Cancel the common factor (x-7).

3)
Factor -1 from the top and factor the bottom.
Cancel the common factor (3x-1).