Question

Show work! :D Medal will be rewarded! :D 28. Split into a sum of two rational expression with unlike denominators: 2x + 3 over x^2 + 3x + 2

Answer 1

partial fraction decomposition?

Answer 2

\[\frac{2x+3}{x^2+3x+2}=\frac{2x+3}{(x+2)(x+1)}\] is a start

Answer 3

\[\frac{ 2x + 3 }{ x^2 + 3x + 2 }\]

Answer 4

it is going to be
\[\frac{A}{x+1}+\frac{B}{x+2}\] and you need to find \(A\) and \(B\)

Answer 5

when you add \[\frac{A}{x+1}+\frac{B}{x+2}\] the numerator will be
\[A(x+1)+B(x+2)\] and that must be equal to \[2x+3\]

Answer 6

you can find \(A\) and \(B\) by choosing suitable values for \(x\) in the equation
\[A(x+1)+B(x+2)=2x+3\]
first choose \(x=-1\) and get
\[A(-1+1)+B(-1+2)=2(-1)+3\] or
\[B=1\]

Answer 7

now let \(x=-2\) to find \(A\)

Answer 8

plug -2 into 2x + 3

Answer 9

Do what satellite said. He gave you this equation:
A(x+1)+B(x+2)=2x+3
and said to let x = -2 to find A