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3 years ago

Hey can you please help me posted picture of question :)

Mathematics

1 answer:

jek_recluse [69]3 years ago

5 0

The sum of a and b will be the coefficient of the x term of the trinomial. This can be seen below.

(x + a)(x + b)
= x² + bx + ax + ab
= x² + (a+b)x + ab

x is being multiplied by both a and b individually and the products are being added, so sum of a and b appears as the coefficient of x term.

Thus the answer to this question is option C

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What is the sum? StartFraction 3 y Over y squared + 7 y + 10 EndFraction + StartFraction 2 Over y + 2 EndFraction

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Answer:

$\dfrac{5}{y+5}$

Step-by-step explanation:

Here, we have to find the sum of 2 fractions:

1st fraction: $\dfrac{3y}{y^{2}+7y+10}$

2nd fraction: $\dfrac{2}{y+2}$

Considering the denominator of 1st fraction:

$y^{2}+7y+10$

Using factorization method:

$7y$ can be written as $(2y + 5y)$ .

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Taking 5 common from $5y+10$ and y common from $y^{2}+2y$ : $\Rightarrow y(y+2)+5(y+2)$

Now taking $(y+2)$ common:

$\Rightarrow (y+5)(y+2)$

$\dfrac{3y}{y^{2}+7y+10}$ can be written as $\dfrac{3y}{(y+5)(y+2)}$

Now, calculating the sum:

$\dfrac{2y}{(y+5)(y+2)} + \dfrac{2}{y+2}$

Taking LCM and solving:

$\Rightarrow \dfrac{3y+2(y+5)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5y+10}{(y+5)(y+2)}\\\Rightarrow \dfrac{5(y+2)}{(y+5)(y+2)}\\\Rightarrow \dfrac{5}{(y+5)}$