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BigorU [14]
3 years ago
12

PLZZ HELPP ASAP MATH QUESTION SIMPLIFY COMPLEX FRACTION

Mathematics
1 answer:
Ksivusya [100]3 years ago
6 0

Answer:

\large\boxed{\dfrac{x^3+6x}{80x+64}}

Step-by-step explanation:

\dfrac{\frac{1}{8}+\frac{x+4}{16}}{\frac{x+4}{x^2}+\frac{4}{x}}=\left(\dfrac{1\cdot2}{8\cdot2}+\dfrac{x+4}{16}\right):\left(\dfrac{x+4}{x^2}+\dfrac{4\cdot x}{x\cdot x}\right)\\\\=\left(\dfrac{2}{16}+\dfrac{x+4}{16}\right):\left(\dfrac{x+4}{x^2}+\dfrac{4x}{x^2}\right)=\dfrac{2+x+4}{16}:\dfrac{x+4+4x}{x^2}\\\\=\dfrac{x+6}{16}:\dfrac{5x+4}{x^2}=\dfrac{x+6}{16}\cdot\dfrac{x^2}{5x+4}=\dfrac{(x+6)(x^2)}{(16)(5x+4)}\\\\\text{use distributive property}\ a(b+c)=ab+ac

=\dfrac{(x)(x^2)+(6)(x)}{(16)(5x)+(16)(4)}=\dfrac{x^3+6x}{80x+64}

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I got the answer as letter C, can someone check me to make sure that is correct? Thank you in advance.
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The x's cancel  so definitely is choice C:  1/9

Step-by-step explanation:

We have   root( 1/(x^2) )  *  root ((x^2) / 81)

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root( 1/(x^2) )  *  root ((x^2) / 81)

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F(x)
mina [271]

a) Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.

b) The function f(x) = \frac{x}{x^{2}+ x} is equivalent to the function g(x) = \frac{1}{x + 1}.

<h3>How to determine whether a limit exists or not</h3>

According to theory of limits, a function f(x) exists for x = a if and only if \lim_{x\to a^{-}} f(x) = \lim_{x \to a^{+}} f(x). This criterion is commonly used to prove continuity of functions.

<em>Rational</em> functions are not continuous for all value of x, as there are x-values that make denominator equal to 0. Based on the figure given below, we have the following <em>lateral</em> limits:

\lim_{x \to -1^{-}} \frac{x}{x^{2}+x} = - \infty

\lim_{x \to -1^{+}} \frac{x}{x^{2}+x} = + \infty

Since both limits are <em>distinct</em> and do not exist, we conclude that x = - 1 is not part of the domain of the <em>rational</em> function.

In addition, we can simplify the function by <em>algebra</em> properties:

\frac{x}{x^{2}+ x} = \frac{x}{x\cdot (x + 1)} = \frac{1}{x + 1}

g(x) = \frac{1}{x + 1}

The function f(x) = \frac{x}{x^{2}+ x} is equivalent to the function g(x) = \frac{1}{x + 1}.

To learn more on lateral limits: brainly.com/question/21783151

#SPJ1

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