What is wrong with the following equation? (x² + x - 42)/(x - 6) = x + 7
(x - 6)(x + 7) ≠ x² + x - 42
The left-hand side is not defined for x = 0, but the right-hand side is.
The left-hand side is not defined for x = 6, but the right-hand side is.
None of these - the equation is correct.

Solution:

Given: Equation is (x² + x - 42)/(x - 6) = x + 7

The first statement is wrong. (x - 6)(x + 7) = x² + x - 42

We know that for a fraction to exist, the denominator should be positive and not equal to 0.

On the right-hand side, we don’t have variables in the denominator so, x + 7 is possible for all x values

On the left side, the denominator is x - 6

⇒ x - 6 > 0; x - 6 ≠ 0

⇒ x > 6; x ≠ 6

Thus x = 6 is the excluded value in the rational expression.

Hence, the left-hand side is not defined for x = 6 but the right hand is. The third statement is correct. the other three statements are wrong.

What is wrong with the following equation? (x² + x - 42)/(x - 6) = x + 7

Summary:

For the given equation (x² + x - 42)/(x - 6) = x + 7, the left hand side is not defined for x = 6 but the right hand is.