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# What is wrong with the following equation? (x^{2} + x - 42)/(x - 6) = x + 7

(x - 6)(x + 7) ≠ x^{2} + 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 (x^{2} + x - 42)/(x - 6) = x + 7

The first statement is wrong. (x - 6)(x + 7) = x^{2} + 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? (x^{2} + x - 42)/(x - 6) = x + 7

**Summary:**

For the given equation (x^{2} + x - 42)/(x - 6) = x + 7, the left hand side is not defined for x = 6 but the right hand is.

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