Rational Functions

Question

The roots of  x+3/3x-2 = -7+x can be determined using which of the following?

The x-intercepts of the function 𝑦 = 𝑥 + 3/3𝑥−2 + 𝑥 − 7

The x-coordinates of the points of intersection of 𝑦=𝑥+3/3𝑥−2 𝑎𝑛𝑑 𝑦=−𝑥−7

The x-coordinates of the points of intersection of 𝑦=𝑥+3/3𝑥−2 𝑎𝑛𝑑 𝑦=𝑥+7

The x-intercepts of the function 𝑦=𝑥+3/3𝑥 −2−𝑥+7

Answer 1

The roots of (x + 3) / (3x - 2) = x - 7 can be determined using which of the following:

1. The x-intercepts of the function 𝑦 = (𝑥 + 3) / (3𝑥 - 2) + 𝑥 - 7
2. The x-coordinates of the points of intersection of 𝑦 = (𝑥 + 3) / (3𝑥 - 2) 𝑎𝑛𝑑 𝑦 = -𝑥 - 7
3. The x-coordinates of the points of intersection of 𝑦 = (𝑥 + 3) / (3𝑥 - 2) 𝑎𝑛𝑑 𝑦 = 𝑥 + 7
4. The x-intercepts of the function 𝑦 = (𝑥 + 3) / (3𝑥 - 2) - 𝑥 + 7

The correct choice is the last one, as that is what we get by taking the right hand side (RHS) to the left side of the equation.