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Home Q & A Board Science-Related Homework Help Mathematics
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leezysosteezy leezysosteezy
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11 years ago
Hi, does anyone know how to solve this equation for variable x?

4/x - 2 + 1/x + 2 = - 4x/x2 - 4

I also need to know the way to write the answer. Thanks
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#1
11 years ago
Is that x^2 or 2x on the RHS of the equation?

-2 and 2+ cancel each other out on LHS
4/x+1/x= 5/x on the LHS

-4x/x2 reduces to -4/x if that is an x^2 on the RHS
move -4/x to the other side to get
9/x=-4 flip it
 to get x/9=-1/4
solve for x to get x= -9/4
Answer accepted by topic starter
8kjw38kjw3
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#2
Posts: 8
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11 years ago
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#3
11 years ago
(4/x) - 2 + (1/x) + 2 = [(-4x)/(x^2)] - 4

I assume that your "x2" means "x^2". If not, let me know, and I'll correct the work and answer.

The first step is to put common denominators on both the right and left side. You do not need to have the same denominators on both sides - just a common denominator for one, and a common denominator for the answer.

(4/x) - (2x/x) + (1/x) + (2x/x) = (-4x/x^2) - (4x^2/x^2)

Now add (and subtract).

(4 - 2x + 1 + 2x) / x = (-4x - 4x^2) / x^2

And simplify.

5 / x = (-4 - 4x) / x

Now you can use cross multiplication to solve this:

(-4 - 4x) * x = 5 * x

Since there is an x on both sides, you can cancel it out.

-4 - 4x = 5

Add 4 to both sides.

-4x = 9

And divide by -4.

x = -9/4

You can write this three ways: -9/4, -2 and 1/4, or -2.25

That is your final answer.
wrote...
#4
11 years ago
first simplify so
5/x = -4/x -4

add 4/x to both sides
9/x = -4

multiply both sides by x
9x/x = 9  so itd be 9 =-4x

divide by -4
9/-4 = x
wrote...
#5
11 years ago
x=2, x=-1/2, x=-2
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