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)
If so, your answer is correct!
If your first problem was this:
(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.
To simplify the expression 8x - 1/x + 5x - 3/2x, you can follow these steps:
Step 1: Find the common denominator.
The denominators in this expression are x and 2x. To find the common denominator, you need to determine the least common multiple (LCM) of x and 2x.
Since 2x is already a multiple of x, the LCM is simply 2x.
Step 2: Rewrite the fractions with the common denominator.
Multiply the numerator and denominator of each fraction by the necessary factors to obtain the common denominator.
For the first fraction, (8x - 1)/x, you need to multiply the numerator by 2 to get 16x - 2, and the denominator by 2 to get 2x.
For the second fraction, (5x - 3)/2x, you don't need to change anything since the denominator is already 2x.
The expression now becomes:
(16x - 2)/(2x) + (5x - 3)/(2x)
Step 3: Combine the fractions.
Since the denominators are now the same, you can combine the numerators and put them over the common denominator.
(16x - 2 + 5x - 3)/(2x)
Simplify the numerator:
(21x - 5)/(2x)
This is the simplified form of the expression.
As for finding the lowest common denominator (LCD) in the second problem, you correctly identified it as 7x(x - 4).
In the third problem, you simplified (3x^2 - 2x)/(15x - 10) to x/5. Well done!
If you have any further questions or need additional assistance, feel free to ask.