Solve the equation (x+2)/(x-3)=(x-6)/(x+1) for x.

We need to multiply both sides by the denominator (the bottom of the fraction) in both fractions so we get:(x+2)(x-3)(x+1)/(x-3)=(x-6)(x-3)(x+1)/(x+1)Now, we can see that we can cancel each fraction to get that:(x+2)(x+1)=(x-6)(x-3)Then expanding these brackets we get:x^2+3x+2=x^2-9x+18Now taking away x^2 from both sides, adding 9x to both sides and taking 2 from both sides we get:12x=16This means that x=16/12=4/3