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Which expression is equivalent to StartFraction 2 a + 1 Over 10 a minus 5 Endfraction divided by StartFraction 10 a Over 4 a squared minus 1 EndFraction?
StartFraction 2 a Over (2 a minus 1) squared EndFraction
StartFraction 50 a Over (2 a + 1) squared EndFraction
StartFraction (2 a minus 1) squared Over 2 a EndFraction
StartFraction (2 a + 1) squared Over 50 a EndFraction

Respuesta :

carlosego

For this case we must simplify the following expression:

[tex]\frac {\frac {2a + 1} {10a-5}} {\frac {10a} {4a ^ 2-1}} =[/tex]

We apply double C:

[tex]\frac {(4a ^ 2-1) (2a + 1)} {10a (10a-5)} =[/tex]

We apply distributive property in the numerator and we take common factor 5 in the denominator:

[tex]\frac {8a ^ 3 + 4a ^ 2-2a-1} {10a (5 (2a-1))} =[/tex]

We factor the numerator:

[tex]\frac {(2a + 1) ^ 2 (2a-1)} {10a (5 (2a-1))} =\\\frac {(2a + 1) ^ 2 (2a-1)} {50a (2a-1)} =[/tex]

We simplify:

[tex]\frac {(2a + 1) ^ 2} {50a}[/tex]

Answer:

[tex]\frac {(2a + 1) ^ 2} {50a}[/tex]

Option D

The expression is equivalent to the [tex]\dfrac{(2a+1)^2}{50a}[/tex].

We have to determine, the expression is equivalent to,

[tex]= \dfrac{\frac{2a+1}{10a-5}}{\frac{10a}{4a^2-1 }}[/tex]

To determine the equivalent expression of the given expression follow all the steps given below.

  • Step1; Apply double C property and written function in the simplest form,

          [tex]= \dfrac{2a+1}{10a-5} \times \dfrac{4a^2-1}{10a}[/tex]

  • Step2; Factorize the term [tex]4a^2-1[/tex] and taking common factor 5 in the denominator.

        [tex]= \dfrac{(2a+1 )\times (2a-1) \times (2a+1)}{10a(5(2a-1))}\\\\= \dfrac{(2a+1 )\times (2a-1) \times (2a+1)}{50a(2a-1)}\\\\[/tex]

  • Step3: Cancel out the (2a-1 )same term from numerator and denominator.

        [tex]= \dfrac{(2a+1 ) \times (2a+1)}{50a}\\\\[/tex]

  • Step4; Multiply the equation and write the equation in simplest form,.

       [tex]= \dfrac{(2a+1)^2}{50a}[/tex]

Hence, The expression is equivalent to the [tex]\dfrac{(2a+1)^2}{50a}[/tex].

To know more about Function click the link given below.

https://brainly.com/question/15186010

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