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Which expression is equivalent to the expression below? StartFraction m + 3 Over m squared minus 16 EndFraction divided by StartFraction m squared minus 9 Over m + 4 EndFraction StartFraction 1 Over (m + 4) (m + 3) EndFraction StartFraction 1 Over (m minus 4) (m minus 3) EndFraction StartFraction m minus 4 Over m minus 3 EndFraction StartFraction m + 3 Over m + 4 EndFraction

Respuesta :

Option B: [tex]\frac{1}{(m-4)(m-3)}[/tex] is the correct answer.

Explanation:

The given expression is [tex]\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}[/tex]

Simplifying the expression, we have,

[tex]\frac{m+3}{m^{2}-16}\times\frac{m+4}{m^2-9}[/tex]

Factor the equations, [tex]m^{2}-16\right[/tex] and [tex]m^{2}-9[/tex],we get,

[tex]m^{2}-16\right=m^{2}-4^{2}=(m+4)(m-4)[/tex]

[tex]m^{2}-9=m^{2}-3^2=(m+3)(m-3)[/tex]

Substituting these factored expressions in the above expression, we have,

[tex]\frac{m+3}{(m+4)(m-4)}\times\frac{m+4}{(m+3)(m-3)}[/tex]

Cancelling the common terms [tex]m+3[/tex] and [tex]m+4[/tex] , we get,

[tex]\frac{1}{(m-4)(m-3)}[/tex]

Thus, the expression equivalent to [tex]\frac{(\frac{m+3}{m^2-16}) }{(\frac{m^2-9}{m+4} )}[/tex] is [tex]\frac{1}{(m-4)(m-3)}[/tex]

Hence, Option B is the correct answer.

adioabiola

The equivalent expression to StartFraction m + 3 Over m squared minus 16 EndFraction divided by StartFraction m squared minus 9 Over m + 4 EndFraction is StartFraction m + 3 Over m + 4 EndFraction

Equivalent expressions to fractions

Given:

  • (m + 3) / (m² - 16) ÷ (m² - 9)/ (m + 4)(m + 3)

Hence, upon evaluation; we have;

  • = (m + 3) / (m² - 16) × (m + 4)(m + 3) / (m² - 9)

  • = (m + 3) / (m² - 16) × (m + 4)(m + 3) / (m² - 9)= (m + 3) / (m² - 16) × (m + 4)(m + 3)) / m² - 9

  • = (m + 3) / (m² - 16) × (m + 4)(m + 3) / (m² - 9)= (m + 3) / (m² - 16) × (m + 4)(m + 3)) / m² - 9= (m + 3) / (m + 4) (m - 4) × (m + 4)(m + 3) / (m + 4)(m - 3)

  • = (m + 3) / (m² - 16) × (m + 4)(m + 3) / (m² - 9)= (m + 3) / (m² - 16) × (m + 4)(m + 3)) / m² - 9= (m + 3) / (m + 4) (m - 4) × (m + 4)(m + 3) / (m + 4)(m - 3)= (m + 3) / (m + 4)

The equivalent expression to the given expression is therefore; m + 3) / (m + 4)

Learn more about equivalent equation:

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