Case 1. Distinct linear factor in denominator
Let us see the how to slove when distinct linear factor is in denominator. Distinct Linear Factor: [latex s= 2]F(x) = \frac{8x-42}{x^2+3x-18}[/latex] [latex s=2]F(x) = \frac{8x-42}{x^2+3x-18} = \frac{8x-42}{(x+6)(x-3)} = \frac{A}{x+6}+\frac{B}{x-3}[/latex] Multiply by [latex]\textbf(x+6)(x-3)[/latex] on both sides with above equation we get [latex s=-1]\Big((x+6)(x-3)\Big)\Big(\frac{8x-42}{x^2+3x-18}\Big) = \Big(\Big((x+6)(x-3)\Big)\Big(\frac{A}{x+6}\Big)\Big) + \Big(\Big((x+6)(x-3)\Big)\Big(\frac{B}{x-3}\Big)\Big)[/latex] [latex]8x-42=A(x-3)+B(x+6)[/latex] …………(1) Now we have [latex]\textbf{(x+6)}[/latex] and […]