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jenyasd209 [6]
3 years ago
14

What is the quotient of the rational expression shown below? Make sure your answer is in reduced form x^2-4/x+3 divided x^2-4x+4

/4x+2
Mathematics
1 answer:
natita [175]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

Given

\frac{x^2-4}{x+3} ÷ \frac{x^2-4x+4}{4x+2}

The first step is to factor numerators/denominators, if possible

x² - 4 = (x - 2)(x + 2) ← difference of squares

x² - 4x + 4 = (x - 2)(x - 2) ← perfect square

4x + 2 = 2(2x + 1)

To divide the expressions follow the steps

• Leave the first fraction

• Change division to multiplication

• Turn the second fraction upside down

We now have

\frac{(x-2)(x+2)}{x+3} × \frac{2(2x+1)}{(x-2)(x-2)}

Final step is to cancel common factors from the numerators/denominators

= \frac{2(2x+1)(x+2)}{(x+3)(x-2)} ← quotient


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6x+4y=42 -3x+3y=-6 by elimination
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Answer:

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Step-by-step explanation:

To solve this system, we need to find x and y. First, let's find x. In the first equation (6x+4y=42), subtract 4y on both sides to isolate 6x. This will result in 6x=42-4y. Divide by 6 on both sides to isolate x and get x=7-\frac{2}{3}y. Now we know what x equals. Go to the second equation ad plug this into it. So instead of -3x+3y=-6, you'll have -3(7-\frac{2}{3}y)+3y=-6. Use the distributive property to get -21+2y+3y=-6. Add 2y and 3y to get -21+5y=-6. Add 21 to both sides to isolate 5y and get 5y=15. Divide by 5 on both sides to isolate y and get y=3. Now that we know that y=3, we can plug this back into the equation that was bolded above so that we can find x, so we'll have x=7-\frac{2}{3}(3) since y=3, and we'll get x=7-\frac{6}{3}, or x=7-2, or x=5.

x=5

y=2

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Answer:

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Step-by-step explanation:

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