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3 years ago

[Algebra 2] Find the quotient with the necessary restrictions.

Mathematics

1 answer:

Tatiana [17]3 years ago

8 0

Answer:

The correct answer is: 3x² (4x - 1) / (x - 4) (x - 3) ∧ restriction x ≠ 3, x ≠ 4, x ≠ 0 and x ≠ 1/4

Step-by-step explanation:

Given:

((16x² - 8x + 1) / (x² - 7x + 12)) : ((20x² - 5x) / 15x³) =

dividing with one fraction is the same as multiplying with its reciprocal value

((16x² - 8x + 1) / (x² - 7x + 12)) · (15x³ / (20x² - 5x))

First we need to factorize both numerators and denominators

16x² - 8x + 1 = (4x - 1)² This is square binomial

x² - 7x + 12 = x² - 4x - 3x + 12 = x (x - 4) - 3 (x - 4) = (x - 4) ( x - 3)

20x² - 5x = 5x (4x - 1)

(4x - 1)² / (x - 4) (x - 3) · 15x³ / 5x (4x - 1)

The existence of this rational algebraic expression is possible only if it is:

x - 4 ≠ 0 and x - 3 ≠ 0 and x ≠ 0 and 4x - 1 ≠ 0 =>

x ≠ 4 and x ≠ 3 and x ≠ 0 and x ≠ 1/4 This is restriction

Finally we have:

3 x² (4x - 1) / (x - 4) (x - 3)

God with you!!!

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Step-by-step explanation:

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3 years ago

Read 2 more answers

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madreJ [45]

Answer:

2. n = 11

4. g = -2

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8. n = 4

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Step-by-step explanation:

2. 63 = -3(1 - 2n)

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$-g+2\times 3 + 2\times g = -4\times g + -4\times 1\\-g+6+ 2g=-4g-4\\\textrm{we will take all the g term the left side and the constant to the right side}\\4g-g+2g=-6-4\\5g=-10\\g=\frac{-10}{5}\\\therefore g=-2$

6.-3(t +5 ) + (4t + 2) = 8

Using distributive property A( B +C) = AB + AC we get

$-3\times t + -3\times 5 + 4t + 2=8\\-3t-15+ 4t + 2=8\\t=8+15-2\\t=21\\\therefore t=21\\$

8. -8 - n = -3(2n -4)

Using distributive property A( B +C) = AB + AC we get

$-8 - n = -3\times 2n - -3\times4\\-8-n=-6n+12\\\textrm{all the n terms to the left inside and the constant of the right-hand side}\\6n-n=8+12\\5n=20\\n=\frac{20}{5}\\ \therefore n= 4$

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Using distributive property A( B +C) = AB + AC we get

$-4\times 2 --4\times y + 3y = 3\times y -3\times 4\\-8+4y+3y =3y-12\\\textrm{all the y terms to the left side and the constant to the right side}\\4y+3y-3y=-12+8\\4y=-4\\y=\frac{-4}{4}\\ \therefore y=-1$

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3 years ago

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earnstyle [38]

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Answer:

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2 years ago

[Algebra 2] Find the quotient with the necessary restrictions.​

[Algebra 2] Find the quotient with the necessary restrictions.