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

Please note that if I apply the least common multiple of both denominators of your expression is:

(x+3) (x+6), so

we can accept all values of x such that x is not equal to -3, and x is not equal to -6.

Next, we can write:

(x-2) (x+1) = (x-1) (x+3)

and applying the distributive property of multiplication over addition at both sides of the last above expression, we get:

x^2 + 4x - 12 = x^2 + 2x - 3

after a simplification, I can write:

4x - 12 = 2x - 3

or:

2x = 9

dividing both sides by 2, I get your answer as below:

x = 9/2

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