Answer:
Noah mistakenly added 25 and 7 in denominator instead of subtracting in the third step.
Step-by-step explanation:
Noah had to rationalize the denominator of [tex]\frac{32}{5-\sqrt{7}}[/tex]
According to him,
[tex]\frac{32}{5-\sqrt{7} = \frac{32(5+\sqrt{7}{(5-\sqrt{7})(5+\sqrt{7}[/tex]
Solving the nominator and denominator
[tex]= \frac{160-32\sqrt{7}}{25+5\sqrt{7}-5\sqrt{7}-7}[/tex]
Noah did correctly till this point.
In the next step he add 25 and 7 in the denominator, whereas, it should be subtracted.
Hence,
Noah mistakenly added 25 and 7 in denominator instead of subtracting in the third step.
