jiaern0405
Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.


[tex] ({4e }^{2} + 16e - 9) \div (2ef + 12e - f - 6)[/tex]
please help me solve this problem​

Sagot :

theleangreenbean

Explanation

[tex]\dfrac{4e^2+16e-9}{2ef+12e-f-6}[/tex]

⇒ First, factor the numerator by grouping:

[tex]=\dfrac{4e^2-2e+18e-9}{2ef+12e-f-6}\\\\\\=\dfrac{2e(2e-1)+9(2e-1)}{2ef+12e-f-6}\\\\\\=\dfrac{(2e+9)(2e-1)}{2ef+12e-f-6}[/tex]

⇒ Now, factor the denominator by grouping:

[tex]=\dfrac{(2e+9)(2e-1)}{2e(f+6)-(f+6)}\\\\\\=\dfrac{(2e+9)(2e-1)}{(2e-1)(f+6)}[/tex]

⇒ We must determine which values of e and f are unacceptable, meaning, will make this expression undefined. These will be the values of e and f that make the denominator equal to 0.

  • ⇒ To find these values, let's set each term in the denominator equal to 0, and solve for e and f.
  • [tex]2e-1=0[/tex] ⇒ [tex]2e=1[/tex] ⇒ [tex]e=\dfrac{1}{2}[/tex]
  • [tex]f+6=0[/tex] ⇒ [tex]f=-6[/tex]
  • ⇒ The restrictions for e and f include [tex]e=\dfrac{1}{2}[/tex] and [tex]f=-6[/tex].

[tex]=\dfrac{(2e+9)(2e-1)}{(2e-1)(f+6)}[/tex]

⇒ Reduce values in the numerator and denominator:

[tex]=\dfrac{(2e+9)}{(f+6)}\\\\\\=\dfrac{2e+9}{f+6}[/tex]

Answer

[tex]=\dfrac{2e+9}{f+6}[/tex]

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.