Alg5.1.4

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If \frac{3x+2}{2-x-x^2}=\frac{A}{2+x}+\frac{B}{1-x}\, What is the value of A?

Given that \frac{3x+2}{2-x-x^2}=\frac{A}{2+x}+\frac{B}{1-x}\,

Equating numerators on both sides 3x+2=A(1-x)+B(2+x)\,

Substituting x=-2\, in 3x+2=A(1-x)+B(2+x)\,

-4=3A\,

The value of A\, is A=\frac{-4}{3}\,


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