What is the quotient in simplified form? State any restrictions on the variable.

Question

What is the quotient in simplified form? State any restrictions on the variable. Show Work. a + 2/a - 5 a + 1 a^2 - 8a + 15 Vance is designing a garden in the shape of an isosceles triangle. The base of the garden is 36 feet long. The function y = 18 tan theta models the height of triangular garden. a. What is the height of the triangle when theta = 45 degree? b. What is the height of the triangle when theta = 55 degree? c. Vance considering using either theta = 45 degree or theta = 55 degree for his garden. Compare the areas of the two possible gardens. Explain how you found the areas.

Explanation / Answer

1) (a+2)/(a -5) / (a+1)/(a^2 -8a +15)

(a+1)/(a^2 -8a +15) = (a+1)/(a^2 -3a - 5a+15)

= (a+1)/(a - 3)(a -5)

(a+2)/(a -5) / (a+1)/(a^2 -8a +15) = (a+ 2)(a-3)(a -5)/(a+1)(a -5)

= (a +2)(a -3)/(a+1)

Restriction : a should not be equal to -1 as this would make denominator 0

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