Question

For the rational function f(x)=x-2/3x^2+x-2, solve f(x)=2

Answer 1

When f(x) = 2, x = 1/2, -2/3

Explanation:

Step 1: Set equation equal to 2

`2 = (x-2)/(3x^2 +x -2)`

Step 2: Multiply both sides by denominator

2(3x² + x - 2) = x - 2

Step 3: Distribute

6x² + 2x - 4 = x - 2

Step 4: Isolate everything to one side

6x² + x - 2 = 0

Step 5: Factor

(2x - 1)(3x + 2) = 0

Step 6: Find roots

x = 1/2, -2/3