Question

final review
session: 4/100 attempt: 1/17
question 2
simplify:
\\(\frac{c^2 + c - 42}{c^2 - 13c + 36} \div \frac{c + 7}{c - 4}\\)

Explanation:

Step1: Factor numerators and denominators

Factor \( c^2 + c - 42 \): find two numbers that multiply to -42 and add to 1. They are 7 and -6. So \( c^2 + c - 42=(c + 7)(c - 6) \).
Factor \( c^2 - 13c + 36 \): find two numbers that multiply to 36 and add to -13. They are -4 and -9. So \( c^2 - 13c + 36=(c - 4)(c - 9) \).

The expression becomes: \( \frac{(c + 7)(c - 6)}{(c - 4)(c - 9)} \div \frac{c + 7}{c - 4} \).

Step2: Change division to multiplication

Dividing by a fraction is multiplying by its reciprocal. So:
\( \frac{(c + 7)(c - 6)}{(c - 4)(c - 9)} \times \frac{c - 4}{c + 7} \).

Step3: Cancel common factors

Cancel \( (c + 7) \) and \( (c - 4) \) from numerator and denominator:
\( \frac{\cancel{(c + 7)}(c - 6)}{\cancel{(c - 4)}(c - 9)} \times \frac{\cancel{(c - 4)}}{\cancel{(c + 7)}}=\frac{c - 6}{c - 9} \).

Answer:

\( \frac{c - 6}{c - 9} \)