What is the least common denominator of the expression below? x2 x2 − 16 + 9 + x 8x + 2x2

1 answer:

eduard2 years ago

7 0

The least common denominator of the rational expression [x²/(x² - 16)] + [(9+x)/(8 · x + 2 · x²)] found by factor their denominators is 2 · (x + 4) · (x - 4).

<h3>How to find a least common denominator of a rational equation</h3>

Rational numbers are formed by numbers of the form n/m, where n and m are integers known as numerator and denominator, respectively. The least common denominator is the least denominator between a group of rational functions such that they get the same denominator.

In this case we have two denominators: x² - 16, 8 · x + 2 · x². We can determine the least common denominator by factoring each expression and discovering known terms:

x² - 16 = (x + 4) · (x - 4)

8 · x + 2 · x² = 2 · x · (x + 4)

The least common denominator of the rational expression [x²/(x² - 16)] + [(9+x)/(8 · x + 2 · x²)] found by factor their denominators is 2 · (x + 4) · (x - 4).

To learn more on least common denominators: brainly.com/question/8393834

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At a point on the ground 80 ft from the base of a tree, the distance to the top of the tree is 11 ft more than 2 times the heigh

Sergio039 [100]

Let h be the height of the tree and d the distance to the top of the tree from the point on the ground. Draw a diagram to visualize the situation:

Since the distance to the top of the tree is 11 ft more than two times the height, then:

$d=2h+11$

Use the Pythagorean Theorem to relate the length of the sides of the right triangle:

$\begin{gathered} h^2+80^2=d^2 \\ \Rightarrow h^2+6400=(2h+11)^2 \\ \operatorname{\Rightarrow}h^2+6400=(2h)^2+2(11)(2h)+11^2 \\ \operatorname{\Rightarrow}h^2+6400=4h^2+44h+121 \end{gathered}$

Notice that we have obtained a quadratic equation in terms of h. Write it in standard form and use the quadratic formula to solve for h:

$\begin{gathered} \Rightarrow0=4h^2+44h+121-h^2-6400 \\ \Rightarrow0=4h^2-h^2+44h+121-6400 \\ \Rightarrow0=3h^2+44h-6279 \\ \Rightarrow3h^2+44h-6279=0 \\ \\ \Rightarrow h=\frac{-44\pm\sqrt{(44)^2-4(3)(-6279)}}{2(3)} \\ \\ \therefore h_1=39 \\ h_2=-53.666.. \end{gathered}$

Since the height of the tree must be positive, the only solution is h=39ft. To the nearest foot, the height of the tree is 39.

Therefore, the height of the tree is 39 ft.