Question

Each problem has 1-2 errors.

1. On a separate piece of paper you need to correctly identify and explain the error in writing.
2. Then you are to correctly solve the problem, showing all of your steps.

Answer 1

Answer:

1. The error occurred during the factoring of the denominator. (See below for the full explanation).

2. The correct factoring of the denominator is (x + 10)(x - 7), and the correct final simplification is (x + 4)/(x - 7). (See below for the full explanation).

Step-by-step explanation:

The error occurred during the factoring of the denominator, where the middle term 3x was split incorrectly. Since the constant term of the quadratic expression is negative (-70), one of its factors should also be negative. Although the factors 7 and 10 were correctly identified, for their sum to be 3, the 7 should be negated.

The correct factoring of the denominator is as follows:

$x^2+3x-70$

$x^2-7x+10x-70$

$x(x-7)+10(x-7)$

$(x+10)(x-7)$

Now, we can substitute the factored forms of the numerator and denominator into the rational expression:

$\dfrac{(x+10)(x+4)}{(x+10)(x-7)}$

Finally, cancel the common factor (x + 10):

$\dfrac{x+4}{x-7}$

Therefore, the correct simplification of the rational expression is:

$\dfrac{x+4}{x-7}$