Some problems provide the opportunity for more than one mistake.

The Goal

Find

Mistake 1

Find the mistake:

(Roll the mouse over the math to see a hint in red)

Correction 1

(Roll the mouse over the area above to see the corrections in blue)

Mistake 2

Find the mistake:

(Roll the mouse over the math to see a hint in red)

Correction 2

(Roll the mouse over the area above to see the corrections in blue)

Explanations

In the first mistake parentheses should have been used around the factor z⁴-5; not using them meant that the 6z factor was not distributed over the whole factor z⁴-5. Use parentheses!

In the second mistake the numerator terms were reversed; this mistake changes the sign of the result. Take care to get the order of the terms correct in the numerator when using the quotient rule.