Question

write the rational expression in the lowest terms.

(a-3)(x+9)
___________
(3-a)(x-y)

Answer 1

This a problem that involves solving a system of equations.\[\frac{ M }{ 3-a } + \frac{ N }{ x-y } = \frac{ (a-3)(x+9) }{ (3-a)(x-y) }.\] At this point, you need to make the denominators of the fractions on the right hand side the same.\[\frac{ M(x-y) }{ (3-a)(x-y) } + \frac{ N(3-a) }{ (3-a)(x-y) }= \frac{ (a-3)(x+9) }{ (3-a)(x-y) }.\]Observe that the numerators of the right hand side are equal to the numerator of the left hand side.\[M(x-y) + N(3-a) = (a-3)(x+9).\]From here, you can divide both sides by a-3 and set that aside as an equation. Do the same thing, but divide by x+9, and set that aside as another equation. Using those two, and the original equations, you should be able to deduce the partial fraction expansion. Good luck!

Answer 2

this is the type of reply i needed. thank you so much!

Answer 3

You're welcome