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qwelly [4]
1 year ago
13

Reduce the rational expression to lowest terms. If it is already in lowest terms, enter the expression in the answerbox. Also, s

pecify any restrictions on the variable.a²-3a-4/a² + 5a + 4Rational expression in lowest terms:Variable restrictions for the original expression: a

Mathematics
1 answer:
givi [52]1 year ago
7 0

Factorize both quadratic polynomials, as shown below

\begin{gathered} a^2-3a-4=0 \\ \Rightarrow a=\frac{3\pm\sqrt{9+16}}{2}=\frac{3\pm\sqrt{25}}{2}=\frac{3\pm5}{2}\Rightarrow a=-1,4 \\ \Rightarrow a^2-3a-4=(a+1)(a-4) \\  \end{gathered}

Similarly,

\begin{gathered} a^2+5a+4=0 \\ \Rightarrow a=\frac{-5\pm\sqrt{25-16}}{2}=\frac{-5\pm3}{2}\Rightarrow a=-1,-4 \\ \Rightarrow a^2+5a+4=(a+1)(a+4) \end{gathered}

Thus,

\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{(a+1)(a-4)}{(a+1)(a+4)}

Therefore, since the denominator cannot be equal to zero.

<h2>The variable restrictions for the original expression are a≠-1,-4</h2>

Then, provided that a is different than -1,

\Rightarrow\frac{a^2-3a-4}{a^2+5a+4}=\frac{x-4}{x+4}<h2>The rational expression in the lowest terms is (x-4)/(x+4)</h2>

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Which expression represents the ratio of the difference of the two means to Sidney's mean absolute deviation
prohojiy [21]

Answer:

The ratio of the difference of the two means to Sidney's mean absolute deviation = \frac{4}{3.28} = 1.2195

Step-by-step explanation:

P.S - The exact question is -

Given - The means and mean absolute deviations of Sidney’s and Phil’s grades are shown in the table below.

                                       Sidney’s Grades           Phil’s Grades

Mean                                     82                                    78

Mean Absolute Deviation      3.28                                 3.96

To find - Which expression represents the ratio of the difference of the two means to Sidney’s mean absolute deviation?

Proof -

Given that Mean of Sidney Grades = 82

                 Mean of Phil's   Grades = 78

So,

The difference of two means = 82 - 78 = 4

Also,

Given, Mean Absolute Deviation of Sydney = 3.28

Now,

The ratio of the difference of the two means to Sidney's mean absolute deviation = \frac{4}{3.28} = 1.2195

4 0
3 years ago
12). In 1991, there were an estimated 235 fish in a lake. In 1996, there were 134
weqwewe [10]

Answer:bless you

Step-by-step explanation:

4 0
2 years ago
Three times the difference of a number and nine.​
Nikitich [7]

Answer:

3*x-9

Difference means subtraction and times means multiplication!

6 0
2 years ago
Y = 3x + 2<br> What is x?
Aliun [14]
That question is impossible because we don’t know what we are trying to solve for it has to be x or y in this scenario it can’t be both we need one to find the other
4 0
2 years ago
Read 2 more answers
Pls help me quickly
Tcecarenko [31]
All real solutions

Everything cancels out once you multiply the top equation by two.
0 = 0 which means all real answers.
I hoping you meant question 3. Good luck!
3 0
3 years ago
Read 2 more answers
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