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3 years ago

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Simplify the rational expression. Find all numbers that must be excluded from the domain of the simplified rational expression.

1 answer:

kifflom [539]3 years ago

8 0

N/D =(x²+4x+4)/(x² - 4)

N= x²+4x+4 = (x+2)²
D = x²-4 =(x-2)(x+2)

N/D = (x+2)²/(x-2)(x+2); simplify by (x+2)

N/D = (x+2)/(x-2)

Domain of x ={x∈R≠3} ; in short x =( -2) should be excluded

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The sum of the squares of two consecutive positive even integers is 52.Find the integers

ankoles [38]

Answer:

The two consecutive positive integers are $4$ and $6$ .

Step-by-step explanation:

Let $x$ be an even integer, then the next even integer is $(x+2)$ .

The sum of the squares of these even integers is $52$ .

We can write the following equation and solve for $x$ .

$x^2+(x+2)^2=52$ .

We expand to get,

$x^2+x^2+4x+4=52$ .

We simplify to get,

$2x^2+4x+4-52=0$ .

This gives us,

$2x^2+4x-48=0$

We divide through by 2 to get,

$x^2+2x-24=0$ .

This is now a quadratic trinomial

We split the middle term to get,

$x^2+6x-4x-24=0$ .

We factor to obtain,

$x(x+6)-4(x+6)=0$

$\Rightarrow (x+6)(x-4)=0$

$\Rightarrow (x+6)=0 or (x-4)=0$

$\Rightarrow x=-6 or x=4$

We discard $x=-6$ since it is not a positive integer.

$\therefore x=4$

Hence the two consecutive positive even integers are,

$4$

and

$4+2=6$

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nekit [7.7K]

The range is 20 darlin

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A .600

B. .400

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A bag of jellybeans has 20 watermelons jellybeans, 45 sour apple jellybeans, 30 orange jellybeans and 5 cotton candy jellybeans.

Ksju [112]

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3 years ago

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Len [333]

Answer: 47/8

Step-by-step explanation: To write a mixed number as an improper fraction, first multiply the denominator by the whole number and then add the numerator. Finally, we will put our new number over our old denominator and we have our answer which is 47/8.

Therefore, $5\frac{7}{8}$ can be rewritten as the improper fraction 47/8.

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3 years ago