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Hatshy [7]
3 years ago
14

6" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
JulijaS [17]3 years ago
3 0
<h2>Answer:</h2><h2>2(x^2 + 2x + 3) or 2(x^{2} + 2x + 3).</h2><h2>~</h2><h3>To find the answer, simply factor 2 out of 2x^2+4x+6 to get your final answer, </h3><h3>2(x^2 + 2x + 3)</h3><h2>~</h2><h3>Thank you for taking the time to read this!</h3><h3><u>And I hope you have a good day, Loves!</u></h3><h3><em><u>Also if I'm right can you let me know, please?</u></em></h3>

<em><u>Also Also if I am right can I please have Brainliest??</u></em>

<u>You don't need to, I'm just glad I could help. ^^</u>

(If I did help-)

And don't forget to eat a full meal, and have at least one cup of water today!

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zmey [24]

Answer:

a=3 and b=5.

Step-by-step explanation:

So I believe the problem is this:

\frac{2(4x+3)}{x-3}(x+7)}=\frac{a}{x-3}+\frac{b}{x+7}

where we are asked to find values for a and b such that the equation holds for any x in the equation's domain.

So I'm actually going to get rid of any domain restrictions by multiplying both sides by (x-3)(x+7).

In other words this will clear the fractions.

\frac{2(4x+3)}{x-3}(x+7)}\cdot(x-3)(x+7)=\frac{a}{x-3}\cdot(x-3)(x+7)+\frac{b}{x+7}(x-3)(x+7)

2(4x+3)=a(x+7)+b(x-3)

As you can see there was some cancellation.

I'm going to plug in -7 for x because x+7 becomes 0 then.

2(4\cdot -7+3)=a(-7+7)+b(-7-3)

2(-28+3)=a(0)+b(-10)

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Divide both sides by -10:

\frac{-50}{-10}=b

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Now we have:

2(4x+3)=a(x+7)+b(x-3) with b=5

I notice that x-3 is 0 when x=3. So I'm going to replace x with 3.

2(4\cdot 3+3)=a(3+7)+b(3-3)

2(12+3)=a(10)+b(0)

2(15)=10a+0

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Divide both sides by 10:

\frac{30}{10}=a

3=a

So a=3 and b=5.

4 0
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Answer:

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