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Sagot :
To determine which expression is equivalent to [tex]\(\frac{m-4}{m+4} \div (m+2)\)[/tex], we need to simplify the given expression step-by-step:
1. Start with the given expression:
[tex]\[ \frac{m-4}{m+4} \div (m+2) \][/tex]
2. Recall that dividing by a number is the same as multiplying by its reciprocal. Using this property, we can rewrite the division as multiplication with the reciprocal of [tex]\(m+2\)[/tex]:
[tex]\[ \frac{m-4}{m+4} \div (m+2) = \frac{m-4}{m+4} \times \frac{1}{m+2} \][/tex]
3. Combine the fractions using the multiplication rule for fractions (multiply the numerators together and the denominators together):
[tex]\[ \frac{m-4}{m+4} \times \frac{1}{m+2} = \frac{m-4}{(m+4)(m+2)} \][/tex]
4. Therefore, the simplified expression is:
[tex]\[ \frac{m-4}{(m+4)(m+2)} \][/tex]
By following these steps, we find that the expression equivalent to [tex]\(\frac{m-4}{m+4} \div (m+2)\)[/tex] is:
[tex]\[ \boxed{\frac{m-4}{(m+4)(m+2)}} \][/tex]
1. Start with the given expression:
[tex]\[ \frac{m-4}{m+4} \div (m+2) \][/tex]
2. Recall that dividing by a number is the same as multiplying by its reciprocal. Using this property, we can rewrite the division as multiplication with the reciprocal of [tex]\(m+2\)[/tex]:
[tex]\[ \frac{m-4}{m+4} \div (m+2) = \frac{m-4}{m+4} \times \frac{1}{m+2} \][/tex]
3. Combine the fractions using the multiplication rule for fractions (multiply the numerators together and the denominators together):
[tex]\[ \frac{m-4}{m+4} \times \frac{1}{m+2} = \frac{m-4}{(m+4)(m+2)} \][/tex]
4. Therefore, the simplified expression is:
[tex]\[ \frac{m-4}{(m+4)(m+2)} \][/tex]
By following these steps, we find that the expression equivalent to [tex]\(\frac{m-4}{m+4} \div (m+2)\)[/tex] is:
[tex]\[ \boxed{\frac{m-4}{(m+4)(m+2)}} \][/tex]
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