Question

what is the solution to the rational expression... 3/x-2=2/x-3

Answer 1

13
-13
0
5

Answer 2

\(\Large \color{MidnightBlue}{\rightarrow 3(x - 3) = 2(x - 2) }\)


\(\Large \color{MidnightBlue}{\rightarrow 3x - 6 = 2x - 4 }\)

1) Subtract 2x from both sides
2) Add 6 to both sides

Answer 3

\[\begin{array}{l} \frac{3}{x-2}=\frac{2}{x-3} \\ \text{Cross multiply:} \\ 3 (x-3)=2 (x-2) \\ \text{Expand out terms on both sides:} \\ 3 x-9=2 x-4 \\ \text{Add }(9-2 x)\text{ \to both sides:} \\ x=5 \\\end{array}\]