Question

Solve for x. x-1=(x^2-4x+3)/(x+2)

Answer 1

`\begin{gathered} x-1=(x^2-4x+3)/(x+2) \\ \Rightarrow(x-1)/(1)=(x^2-4x+3)/(x+2) \\ \text{Cross multiplying} \\ \Rightarrow x^2-4x+3=(x-1)(x+2) \\ =x(x+2)-1(x+2) \\ =x^2+2x-x-2 \\ =x^2+x-2 \end{gathered}`

That is

`\begin{gathered} x^2-4x+3=x^2+x-2 \\ \Rightarrow x^2-4x+3-x^2-x+2=0 \\ \text{Collecting like terms, we have:} \\ x^2-x^2-4x-x+3+2=0 \\ -5x+5=0 \\ -5x=-5 \\ (-5x)/(-5)=(-5)/(-5) \\ x=1 \end{gathered}`