I need some help with these

Question

1)Find the error in the work shown. Explain the error completely and what should have been done instead. Enter the simplification process.

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simplify:

x^2+2x-8/x^2+6x-16= 1/3x+2

2)Divide the expression below.Simplify completely.

x^2-9/x^2+x-2÷x^2+x-12/x^2+6x+8

Answer 1

1) First factor the numerator and denominator which gives you (x+4)(x-2)/(x+8)(x-2). The (x+2) in the numerator and denominator cancel each other out so final result is (x+4)/(x+8) for all x’s except 2 and -8 as these values make the denominator 0

2) When you divide by a fraction you flip the fraction and multiply so this gives you

(x^2-9)(x^+6x+8)/ (x^+x-2)(x^2+x-12). Now factor all the expressions to get

(x+3)(x-3)(x+4)(x+2)/ (x+2)(x-1)(x+4)(x-3) which reduces to (x+3)/(x-1) for all x’s except 1,-2,3 and -4 as these will make the denominator equal to 0 at some point in the calculation