Corrected Question: subtract Fraction?

Question

5a -12 over a^2 - 8a + 15 minus 3a - 2 over a^2 - 8a + 15

One other:
How do you simplify 18x over 2x - 5 ?

Answer 1

((5a-12)/(a^2-8a+15) -(3a-2)/(a^2-8a+15)
=(5a-12)/(a-3)(a-5) - (3a-2)/(a-3)(a-5)
={5a-12)-(3a-2)/(a-3)(a-5)
=(5a-12-3a+2)/(a-3)(a-5)
=(2a-10)/(a-3)(a-5)
=2(a-5)/(a-3)(a-5)
=2/(a-3) [after cancellation of a-5 from both numerator and denominator]

Answer 2

(5a-12) / (a^2 - 8a + 15) - (3a-2) / (a^2 - 8a + 15)
Both fractions have the same denominator, so we get
= [(5a-12)-(3a-2)] / (a^2 - 8a + 15)
Simplify the top and factorise the bottom:
= (2a - 10) / [(a-3)(a-5)]
= 2(a-5) / [(a-3)(a-5)]
Cancel out the common factor:
= 2 / (a-3), for a not equal to 5.

18x / (2x - 5): note that 18x = 9(2x-5) + 45, so
18x / (2x - 5) = [9(2x-5) + 45] / (2x-5)
= 9 + 45/(2x - 5).

Answer 3

on the first one - you have common demonimators, so just combine your numerators (5a-12) - (3a-2) and put it over the a^2-8a+15. ... but then you might be able to factor that denominator ... perhaps (a-3)(a-5) ... can you factor something out of the numerator so that you can cancel one of the factors on the denominator?

On the second one, you can't simplify it any further.