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I'm new to this site, and here is a question I am stuck on. 

 

https://lh3.googleusercontent.com/-vtEFU5mCcr4/YAJn0Xj9wrI/AAAAAAAAB90/T9sJ4XiWsjg27aNHhVSeQIJ4khhWZO4fgCK8BGAsYHg/s0/2021-01-15.png

 

I am trying to multiply everyone out but I always can't seem to solve it. Any help would be appreciated!

 Jan 16, 2021
 #1
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First, multiply the whole equation by \((x-3)^2(x+5)\):

\(1 = A(x-3)^2+B(x+5)(x-3)+C(x+5)\\ \)

If we set x to be -5, we make B and C equal to zero, which we can use to solve for A:

\(1=A(-5-3)^2\\ 1=A(-8)^2\\ 1=64A\\ \boxed{A=\frac{1}{64}}\)

 Jan 16, 2021

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