Rational expressions

Question

1. Find the error in the work shown below. Explain the error completely and what should have been done instead. Finally, enter the correct simplification process.

2. Divide the expression shown, then simplify completely. Enter all work.

Answer 1

The error in number 1 is that the rational expression is dividing each term separately, this is not allowed. What should be done first is factoring the numerator and denominator completely if possible, then simplify by cancellation.

Number 2: factor each rational expression completely first. Next, change the operation from division to multiplication, and take the reciprocal(flip) of the rational expression that follows. Simplify by cancellation, then multiply straight across with what's left from both rational expressions.

I hope this sparked some ideas?