Intermediate Algebra

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Am I going in the right track?

8x -1/x + 5x - 3/2x

= 16x^2 - 2x/2x^2 + 5x^2 - 3x/2x^2

16x^2 - 2x + 5x^2 - 3x/2x^2

=21x^2 - 5/2x^2

Find the LCD

6/7z- 28, 8/x^2 -4x

= 7x(x-4)

Simplify

3x^2 - 2x/15x-10

= x/5

Let's start by looking at your first problem:

8x -1/x + 5x - 3/2x

To simplify, use a common denominator, which is 2x.

16x^2/2x - 2/2x + 10x^2/2x - 3/2x

Now we have:

(16x^2 - 2 + 10x^2 - 3)/2x

Combining like terms in the numerator:

(26x^2 - 5)/2x

And that's as far as we can go on this one.

Is your second problem supposed to be 6/(7x - 28), 8/(x^2 - 4x)?

If so, your LCD is correct!

For your third problem, I'm going to assume it is this:
(3x^2 - 2x)/(15x - 10)

(8x - 1)/x + (5x - 3)/2x

...then your answer is close. The common denominator would still be 2x, but the answer would be (21x - 5)/2x instead.

I hope this helps.

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