Mathematics, 22.05.2020 06:00, koryn4880

Perform the indicated operation and simplify your answer in factored form.

a^2+6a-7/2a^2+4a^2+2a*2a/a^2-1

Answers: 3

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answered: hrijaymadathil

$\frac{(a-1)(a+7)(a-1)}{4a^{2}(a+1) }$

Step-by-step explanation:

The given expression is

$\frac{(a^{2} +6a-7)}{\frac{(2a^{3} +4a^{2} +2a)(2a)}{(a^{2} -1)} }$

First, we solve the division

$\frac{(a^{2} -1)(a^{2} +6a-7)}{(2a^{3} +4a^{2} +2a)(2a)}$

Second, we factor the numerator

$(a^{2} -1)(a^{2} +6a-7)=(a+1)(a-1)(a+7)(a-1)$

The first expression is the difference between two perfect squares, and the second expression is about finding to number which product is 7 and which difference is 6.

Third, we factor the denominator

$(2a^{3} +4a^{2} +2a)(2a)$

We extract the common factor from the trinomial

$2a(a^{2}+2a+1 )(2a)=4a^{2}(a^{2}+2a+1 )$

Now, we find two number which product is 1 and which sum is 2

$4a^{2}(a^{2}+2a+1 )=4a^{2}(a+1)(a+1)$

Then, we replace all factor in the initial fraction

$\frac{(a+1)(a-1)(a+7)(a-1)}{4a^{2}(a+1)(a+1) }$

Equal factors are simplified, given as result

$\frac{(a-1)(a+7)(a-1)}{4a^{2}(a+1) }$

Therefore, the answer in factored form is

$\frac{(a-1)(a+7)(a-1)}{4a^{2}(a+1) }$

answered: Guest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

answered: Guest

i get you, what you should do is think of the positive things that would come out of it. it will make yours parents proud and raise your grade. you should always try and if you can't focus tell the teacher.

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Perform the indicated operation and simplify your answer in factored form.

a^2+6a-7/2a^2...