SOLUTION: Subtract. Write answer in simplest form. 5a - 12/a^2 - 8a + 15 minus 3a -2/a^2 - 8a + 15 Thanks!

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Question 41238This question is from textbook Beginning Algebra
: Subtract. Write answer in simplest form.
5a - 12/a^2 - 8a + 15 minus 3a -2/a^2 - 8a + 15
Thanks!
 This question is from textbook Beginning Algebra

Answer by zeynep(43)   (Show Source): You can put this solution on YOUR website!
5a - 12/a^2 - 8a + 15 minus 3a -2/a^2 - 8a + 15
I understand the question like this;
(5a - 12)/(a^2 - 8a + 15) minus (3a -2)/(a^2 - 8a + 15)
Since the denominators are the same we can subtract the numerators from each other;
((5a - 12)-(3a -2))/(a^2 - 8a + 15)= (5a-12-3a+2)/(a^2 - 8a + 15)=
(2a-10)/(a^2 - 8a + 15)
Now let's factor the numerator;
2a-10 = 2(a-5)
And if we factor the denominator;
a^2 - 8a + 15=(a-3)(a-5)
So now we have;
2(a-5)/(a-3)(a-5) (if we divide out the common factor (a-5), we get)
2/(a-3)






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