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Stella [2.4K]
3 years ago
15

What is the solution for the equation -3d/d^2-2d-8 + 3/d-4 = -2/d+2

Mathematics
1 answer:
olasank [31]3 years ago
8 0

-3d/(d^2-2d-8) + 3/(d-4) = -2/(d+2)

factor

-3d/(d-4) (d+2) +3/(d-4) = -2/(d+2)

multiply by (d-4)(d+2) on each side

(d-4)(d+2)[-3d/(d-4) (d+2) +3/(d-4)] = (-2/(d+2))*(d-4)(d+2)

distribute

-3d +3(d+2) = -2(d-4)

distribute

-3d +3d+6 = -2d+8

combine like terms

6 = -2d+8

subtract 8 to each side

-2 = -2d

divide by -2

1 =d

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k0ka [10]

We can rewrite the expression under the radical as

\dfrac{81}{16}a^8b^{12}c^{16}=\left(\dfrac32a^2b^3c^4\right)^4

then taking the fourth root, we get

\sqrt[4]{\left(\dfrac32a^2b^3c^4\right)^4}=\left|\dfrac32a^2b^3c^4\right|

Why the absolute value? It's for the same reason that

\sqrt{x^2}=|x|

since both (-x)^2 and x^2 return the same number x^2, and |x| captures both possibilities. From here, we have

\left|\dfrac32a^2b^3c^4\right|=\left|\dfrac32\right|\left|a^2\right|\left|b^3\right|\left|c^4\right|

The absolute values disappear on all but the b term because all of \dfrac32, a^2 and c^4 are positive, while b^3 could potentially be negative. So we end up with

\dfrac32a^2\left|b^3\right|c^4=\dfrac32a^2|b|^3c^4

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3 years ago
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F= 3x^2

Step-by-step explanation:

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2) Similarly in this problem  you would determine the missing factor by dividing the product from -10x^3

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-30x^5 / -10x^3

4) -30 divided by -10 is 3 and as mentioned in step number one, you subtract exponents whenever they are divided by each other.  5-3=2

5) Due to all of the steps mentioned above, The answer is 3x^2

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